고등RPM수1해(002~033)

Transcription

1 고등RPM수해(00~0) 0.6. :0 PM 페이지 다민 50DPI 75LPI 하나를 알면 0개, 0개를 풀 수 있는 개념원리수학 RPM 개념원리수학 익힘책 [알피엠] 수학Ⅰ 정답과 풀이

2 RPM A-B =( - ++)-( - -) = = B-(A+B) =5B-A-B=-A+B =-( - ++)+( - -) = = a _5a =-5a 000 (-5 ) _(- ) =5 _(- fl ) (-5 ) _(- ) = fi = 0005 (-a b) (-a b ) =(-a b ) a b (-a b) (-a b ) =-;Åb; 0006 ( ) _(- ) (- ) = fl _fl (- fl ) = ( -+)= ( +)( -+) = = ( +)+(- +) = = ( -+)(+)-(+) = = - 00 (6 + -) 6 = + - = +-;@; 00 (6a b+afi b -0a b ) a b 6a b afi b 0a b = + - a b a b a b =+a b-5b < , < , (+) =() + + = ++ (-) =() - + (-) =9-6+ (+)(-)=() - =9 - (+)(+)= +(+)+ (+)(+)= +5+6 (+5)(+) = +(8+5)+5 =6 ++0 (--z) =() +(-) +(-z) + (-) + (-) (-z)+ (-z) = + +9z -+6z-z (+) = (+) = + ++ (-) = (-) = (a+)(a -a+)=a + =a +8 (-)( ++)=() - =8 - (+)(+)(+) = +(++) +(+6+)+ =

3 009 ~ 00 (a-b+)(a +b +ab-a+b+) =a +(-b) + - a (-b) =a -b ++ab ( +6+9 )( -6+9 ) =() +() () +() = =t ( ++)( ++) =(t+)(t+)=t +t+ =( +) +( +)+ = = =t ( ++)( -+) =(t+)(t-)=t -9 =( +) -9 = = =(+) - = - (-)= + =(+) -(+) + = - (-) + = =(-) + =(-) + = - =(-) +(-) - =(-) + (-) - =-6-6= ={+;[!;}-= -= {-;[!;}={+;[!;}-= -= -;[!;= 'ß= ' ' 00 A-(X-B)=A A-X+B=A, X=B-A X=B-A=( +- )-( -+ ) = B=- +- A+(- +-)= +-5 A= - A+B=( -)+(- +-) =6 +-9=a +b+c a=6, b=, c=-9 a+b+c= B A=B+A B A=(- +-)+( -+) B A=- +-5 A (B A)=( -+) (- +-5) =( -+)-(- +-5) = (-) =() - + = -+ (+) =() + () + () +() (+) = (-+z) = +(-) +z + (-)+ (-) z+ z = + +z --z+z (++z)( + +z --z-z) = + +(z) - z = + +8z -6z ( ++ )( -+ ) ={() + + }{() - + } =() +() + =6 + + A+B= > A- B =8-6 - A-B= a +b +c =(a+b+c) -(ab+bc+ca) a +b +c =9-8= (A+B)-(B+C) =A+B-B-C =A+B-C =( -)+( +- )-(- ) = = (-)(+)(-) = +(-+-) +{(-) + (-) = = (-+)( ) +(-) (-)}+(-) (-) ={+(-)+}{ +(-) + - (-) = = +(-) + - (-) = (-) - } 00

4 RPM (a-b)(a+b)(a +b )(a +b ) =(a -b )(a +b )(a +b ) =(a -b )(a +b ) =a -b a -b 008 (+)(-)( ++ )( -+ ) ={(-)( ++ )}{(+)( -+ )} =( - )( + ) =( ) -( ) =fl -fl a +ac+c -b =b -(a -ac+c ) a +c =b ABC b B=90 00 (++ + )(++ + ) + + = +6 + = (+)(9 -+ )-(-)( ++9 ) =(+){() - + }-(-){ + +() } =() + -{ -() } =7 + -( -7 ) =6 +8 =a +b a=6, b=8 a-b= (-) (-) ={() -() + -}( -+) =( )( -+) 7 +(-7 ) (-)+9 = = (-)(-5)(-)(+) ={(-)(-)}{(-5)(+)} =( -+)( --5) =(X+)(X-5) -=X =X -X-5 =( -) -( -)-5 = = =t ( ++)( +-)=(t+)(t-)=t -t- =( +) -( +)- = = + -- =a + +b +c- a=, b=0, c=- a-b+c=0 006 ( -+)( -+k) k+(-) (-)+ =(k+) 0 k+=0 k=8 - k+ (-)=(-k-) -k-=-8-=-9-9 k 0% k 0% k 0% 0% 00 (a+b-c )(a-b+c )={a+(b-c )}{a-(b-c )} b-c =t ()=(a+t)(a-t)=a -t =a -(b-c ) =a -(b -bc +c ) =a -b -c +bc 00 (a+b+c)(a-b+c)=(a+b-c)(-a+b+c) {(a+c)+b}{(a+c)-b}={b+(a-c)}{b-(a-c)} (a+c) -b =b -(a-c) -=X ( -+)( -+k) =(X+)(X+k)=X +(k+)x+k =( -) +(k+)( -)+k =( - + )+(k+) -(k+)+k = - +(k+) -(k+)+k 0 k+=0 k=8 -(k+)=-9 00

5 00 ~ ( ) =( )( ) fi =fi +6fi +6fi +fi =0fi fi P=(+)( +)( +)( +) P=(-)(+)( +)( +)( +) P=( -)( +)( +)( +) P=( -)( +)( +) P=( -)( +) P= fl - P+= fl =, 000= ( )( )( ) =(-)(+)( + ) =( - )( + ) = - = m=, n= m+n= _8 =(-)(+)(9+)(8+) =(-)(+)( +)( +) =( -)( +)( +) =( -)( +) = =(+) -(+) = - =- + (+) - + = 5 = - (-) = = a=+', b=-' a-b=', ab= a -b =(a-b) +ab(a-b) a -b =(') + ' a -b ='+6'=0' 005 (+) = ++ ('5) =7+ =- + =( + ) - =7 - (-) = (a+b+c) =a +b +c +(ab+bc+ca) =6+(ab+bc+ca) ab+bc+ca=- a +b +c =(a+b+c)(a +b +c -ab-bc-ca)+abc 8= {6-(-)}+abc abc=-6 abc=- 007 (a+b+c) =a +b +c +(ab+bc+ca) =8+(ab+bc+ca) ab+bc+ca= (ab+bc+ca) =a b +b c +c a +(ab c+abc +a bc) (ab+bc+ca) =a b +b c +c a +abc(a+b+c) =a b +b c +c a + (-) a b +b c +c a = =a 0 +98_0=(a+) +(a-)(a+) =a +a++(a -) =a +a- =_00 +_00- = =(+) - = - =-;#; + =(+) -(+) + = - {-;#;} + =: : 008 a-b=, b-c= a-c=5 c-a=-5 a +b +c -ab-bc-ca =;!;{(a-b) +(b-c) +(c-a) } =;!;{ + +(-5) }=9 a+b+c= a+b=-c, b+c=-a, c+a=-b a +b +c =(a+b+c) -(ab+bc+ca) 5= -(ab+bc+ca) ab+bc+ca= (a+b)(b+c)(c+a) =(-c)(-a)(-b) = - (a+b+c)+(ab+bc+ca)-abc = =

6 RPM (a+b+c)=6 a+b+c= (ab+bc+ca)= ab+bc+ca=6 a +b +c =(a+b+c) -(ab+bc+ca) = - 6= ={+;[!;}- ={+;[!;}-, {+;[!;}=5 +;[!;='5 ( >0) + ={+;[!;}-{+;[!;} + =('5) -'5=5'5-'5 + =' = ;[!;=0 +;[!;= + 5 ={+;[!;}-= -= =+ +0 =+;[!; -;[!;= + + -;[!;+ 5-5 ={-;[!;}+{ + 5 }+{ - 5 } ={-;[!;}+[{-;[!;}+]+[{-;[!;}+{-;[!;}] =+( +)+( + ) = A-{A-(B+C)}-(B+C) =A-A+(B+C)-B-6C =A-A+B+8C-B-6C =A+B+C =( -+ )+( +- )+(- +- ) = =A( +-) =A( +-) < A= (-) =() - () + () -() = (-) (-)(+)( +)( +)( +)( fl +) =( -)( +)( +)( +)( fl +) =( -)( +)( +)( fl +) =( -)( +)( fl +) =( fl -)( fl +) = {-;[!;}={+;[!;}-= -=5 > ;[!;<, -;[!;>0 -;[!;='5-5 ={+;[!;}{-;[!;}=' k+ (- )- =(k-5) k-5= k=8 k= (-) =(+) - 0= - =- + =(+) -(+) = - (-) =

7 0 ~ a +5a-=0 a +5a= (a+)(a+)(a+)(a+) ={(a+)(a+)}{(a+)(a+)} =(a +5a+)(a +5a+6) =(+)(+6) a +5a= =5 006, += +=7 + = + =69 + =(+) - 69=7 -, =0 = ={-;[!;}+= += --+;[!;+ 5 ={ + 5 }-{-;[!;}- = -- = 006 +=, = -(') = + (+) - + = = - = = 0065 ( ) =( )( ) fl =5fl +6fl +5fl =6fl fl (a+b+c) =a +b +c +(ab+bc+ca) 5 =9+(ab+bc+ca) ab+bc+ca=8 ab+bc+ca ;a!;+;b!;+;c!;= = abc 8 = abc= abc ={+ } - 7={+ } -, {+ } =9 + = ( >0) + ={+ } -{+ } = - = a +b +c =(a+b+c) -(ab+bc+ca) 5= -(ab+bc+ca) ab+bc+ca= a +b +c =(a+b+c)(a +b +c -ab-bc-ca)+abc =(5-)+abc abc= 0069 a +b +c -ab-bc-ca =;!;(a +b +c -ab-bc-ca) =;!;{(a -ab+b )+(b -bc+c )+(c -ca+a )} =;!;{(a-b) +(b-c) +(c-a) }=0 a, b, c (a-b) æ0, (b-c) æ0, (c-a) æ0 (a-b) =0, (b-c) =0, (c-a) =0 a=b, b=c, c=a ABC a=b=c 0070 a +b =(a+b) -ab 6= -ab ab=- a +b -ab={(a+b) -ab(a+b)}-ab = - (-) -(-) =5 007 ( +-5) =aº+a +a +a +a +a fi +a fl aº+a +a +a +a +a +a = aº+a +a +a +a +a +a =(+-5) =(-) =- - aº+a +a ++a««, aº+a +a ++a«, = 007 {+;[!;}={-;[!;}+ =('5) +=9 +;[!;= ( >0) 007

8 RPM + 5 ={+;[!;}-{+;[!;} = - =8 007 a+b+c= a+b=-c, b+c=-a, c+a=-b (a+b)(b+c)(c+a) =(-c)(-a)(-b) = - (a+b+c)+(ab+bc+ca)-abc = =6 007 ( ++) ={( +)+} =( +) +( +) +( +)+ =(fl +fi + + )+( + + )+( +)+ =fl +fi fi a=, b=6 ab= a_a_(a-)=a -a (a-) =a -9a +7a-7 (a -a )-(a -9a +7a-7) =6a -7a ;[!;+;]!;= = 5= = + =(+) -(+) + = - = (+)(-)(+)(-) ={(+)(-)}{(-)(+)} =( --)( --8) 8 0% + 0% + 0% -=t ()=(t-)(t-8) ()=t -t+ ()=( -) -( -)+ ()= a=-, b= a+b=8 8 0% 0% a, b 0% a+b 0% '-'=, -'+'= += ={+('-')}{-('-')} = -('-') =-(5-'6) =-+'6 (+'-') +(-'+') = + =(+) -(+) = - (-+'6) =8-(-+'6) =-'6 -'6, +, 0% + 0% + 0% 0079,, a, b, c " a +b +c ='ß a +b +c = (ab+bc+ca)= ab+bc+ca= 008

9 06 ~ 07 (a+b+c) =a +b +c +(ab+bc+ca) =+ =6 a+b+c=6 (a+b+c)= 6= a, b, c a +b +c 0% ab+bc+ca 0% a+b+c 0% 0% 008 (a+b+c) =a +b +c +(ab+bc+ca) =a +b +c + 5 a +b +c =6 a +b +c -ab-bc-ca =;!;{(a-b) +(b-c) +(c-a) } 6-5=;!;{(a-b) +(b-c) +(c-a) } (a-b) +(b-c) +(c-a) = =(+) - = - =-;!; + =(+) -(+) = - {-;!;} =;%; 0080 a +b +c =(a+b+c) -(ab+bc+ca) =0 - (-)=8 a b +b c +c a =(ab+bc+ca) -(ab c+abc +a bc) =(ab+bc+ca) -abc(a+b+c) =(-) - abc 0=6 a +b +c =(a +b +c ) -(a b +b c +c a ) =8-6 = = ;[!;=0 +;[!;= {-;[!;}={+;[!;}- = -=5 > ;[!;<, -;[!;>0 -;[!;='5 + =( + ) - = - {-;!;}=;&; = ( + )+ ( + ) =( + )( + ) =;%; ;&;=: : '5+=0 +0 +'5+;[!;=0 +;[!;=-'5 + 5 ={+;[!;}- =(-'5) -= + 5 ={ + 5 }- = -=7 + 5 ={ + 5 }- =7 -=7-5 ={-;[!;}+{-;[!;} =('5) +'5=8' =0, + -6=0 +=, + =6 + =(+) -(+) 6= - =- + =(+) - = - (-)=0 ( + )( + )=fi +fi + (+) 0 6=fi +fi +(-) fi +fi = 009

10 RPM (-) +-= -++- (-) +-= - (+)(-)= --6 (-)+5=+ (-8)+0= -8+0,, 0087 a+c=0, -(b-)=0, a-b=0 a=6, b=, c= (-)(a+)=a +(-a)-6 a +(-a)-6= +b+c a=, -a=b, -6=c a=, b=-, c=-6,, 0089 =0, =, = -c=, b=, a+b+c=7 a=, b=, c= a(+) +b(+)+c=a +(a+b)+a+b+c ++5=a +(a+b)+a+b+c a=, a+b=, a+b+c=5 a=, b=-, c=6 009, (a+b+)-(a+b+)=0, a+b+=0, a+b+=0 a=-, b= 009 a(-)-b(+)-=(a-b)-(a+b)- (a-b)-(a+b)-=-9+c, a-b=, -(a+b)=-9, c=- a=6, b=, c=- 009 f()= f() - f()=-+5-6= f()= -+;!; f() - f{;!;}= {;!;}- ;!;+;!;= f()= +a ++ f(-)= -8+a-+= a= 0096 f()= -5 +k- f()=0 6-0+k-=0 k=;&; ;&; (-)(+) Q(), a+b (a, b ) + -=(-)(+)Q()+a+b = 0=a+b =- =-a+b, a=-, b= (+)(-) Q(), a+b(a, b ) =(+)(-)Q()+a+b =- -a+b=- = a+b=, a=, b= f()= f()=5-5++=+0 f()=-5++=0 - f() f(0)=+0 00

11 09 ~ 00 f(-)=-6-0-+=-6+0 f(-)=-5-5-+= k=, a=, b=6, c=7, d= , ;#; ;#; - ;#; - 6 ;#; , a, b 0% a, b 0% a-b 0% 006 a =a+ b=b+b =+ (a )-( b)=(a+)-(b+b) (a )-( b)=(a-b+)-b (a )-( b)=+ a-b+=, -b= a=-, b=- a+b=- 007 = c= = b+c= +, b+=5 b= =0 a-b+c=, a-+= a= a +b +c =+9+= 00 (+)(+a)= +(+a)+a = +b+6 +a=b, a=6 a=, b=5 a+b=8 00 ( -)( +)= + -6 = -a +b =-a, -6=b a=-;!;, b=-6 a-b= a(+)-b(-)=(a-b)+(a+b) a(+)-b(-)=+5, a-b=, a+b=5 a=, b= a-b= 008 =a a +=0 a =- =b b +=0 b =- =c c +=0 c =- a +b +c =- 009 =0 =-c c=- = =a a= =- 8=b b= a+b+c= 00 fi -a +b=(+)(-)f()+ =-, =- --a+b=- a=b = -a+b= a-b=0, a=0, b=0 0

12 RPM fi -0 +0=(+)(-)f()+ = -0+0=(+)(-)f()+ -f()=0 f()=0 0 0 k (-+)k+(--7)=0 k -+=0, --7=0 =8, =9 +=7-6a+b=0, a-5=0 a=5, b=0 a+b= =+ =+ a(+)-b+6=0 (a-b)+a+6=0 a-b=0, a+6=0 a=-, b=- ab=8 8 0, (a+b)+(-a+b)+(a-b)=-+-c, a+b=-, -a+b=, a-b=-c a=-, b=-, c= a-b+c= 0 k ( -)k+ -8=0 k -=0, -8=0 =, = = +(m-)+(m+)p+q=0 m (+p)m+(p+q-)=0 m +p=0, p+q-=0 p=-, q= p+q= 08 += =- a +(-)+(-) -b+c(-)+=0 a -(b+c+)+(c+)=0 a=0, b+c+=0, c+=0 a=0, b=, c=- a-b+c=- 09 = fi =aº+a ++a +a =- 0=aº-a ++a -a - fi =(a +a ++a +a ) a +a ++a +a = 00 =0 (0+0+)fi =a º+aª++a +aº aº+a ++aª+a º= 05 -= =+ a +a+b(+) -c-(+)-=0 (a+b) +(a+b-c-)+b-=0 a+b=0, a+b-c-=0, b-=0 a=-, b=, c=- a+b+c=- 06 += =- a(-)+b=5 (-6a+b)+a-5=0 0 ( - ++) (-) =a ª +a ++a +aº (, aº, a,, a, a ª ) aº+a ++a +a ª = (-++) (-) =8 0% = 60% 8 0

13 00 ~ 0 0 = fi +=a º+a ª+a ++a +aº =0 =a º-a ª+a --a +aº - fi =(a ª+a +a ++a +a ) a ª+a ++a +a = 0 +a+b -+ +q (q ) +a+b=( -+)(+q), +a+b= +(q-) +(-q)+q 0=q-, a=-q, b=q q=, a=0, b= a +b = + -+ < + + (-)a+ b - +(a-) + +(a-)+ b + -(a) a+(b-) 0 a+(b-)=0 a=0, b= a +b = - ++b < + (a- (-+a-8) (a(-)b - +(a(a-b)-8)-8 - -(a--6--8b - (a-b+6)-8+b + (a-b+6)-8+b=+ a-b+6=, -8+b= a=-0, b= a+b=-7 06 p+q (p, q ) +a ++=( -)(+)+p+q = - +(p-8)+q a=-, p-8=, q= a=-, p=0, q= a=-, 0+ a=-, f(), g() -, - f()=, g()=- f()+g() - f()+g()= + (-)= 0 Q() +a +b=( +-)Q()++ =(+)(-)Q()++ =- -8+a+b=- = +a+b=5, a=, b= ab= 05 +q (q ) +a-8=( ++b)(+q)++ +a-8= +(q+) +(q+b+)+bq+ 0=q+, a=q+b+, -8=bq+ q=-, a=-0, b= a+b=-7 08 f() +- Q() f()=( +-)Q()+- f()=(-)(+)q()+- f() - f{;!;} f{;!;}= ;!;-= 09 f() + -8 f(-)=-8 (+)f() + (-+)f(-)=- (-8)= f()= + ++ f(-)=+(-)+(-)+ f(-)=- 0 f()= +a +b - f()=+a+b-= 0

14 RPM a+b= f(-)=-a+b-=- -a+b=-, a=, b= ab= 0 f()= + -a+5 f()=+-a+5=0-a f(-)=-8+6+a+5=+a f()=f(-) 0-a=+a a=- 0 f()=afi +b +c- f()=a+b+c-= a+b+c=7 f() + f(-) f(-)=-a-b-c- f(-)=-(a+b+c)- f(-)=-7-=- - 0 (+)f() - (+)f()=f()= f()=+a+b= a+b=- (-)f() + 6 (--)f(-)=6 f(-)=- f(-)=-a+b=- a-b=, a=0, b=- a +b =9 R()=6+6 R()=6 +6=6 07 f() -+ Q () f()=( -+)Q ()+ f()=(-)(-)q ()+ f()= f() -- Q () f()=( --)Q ()+- f()=(-)(+)q ()+- f()=9 f() -5+6 Q(), a+b (a, b ) f()=( -5+6)Q()+a+b f()=(-)(-)q()+a+b f()=a+b= f()=a+b=9, a=5, b= f() 0% f() 0% f() % 0% 05 f() ++, (+)(+) Q(), a+b (a, b ) f()=(+)(+)q()+a+b f(-)=-a+b= f(-)=-a+b=-, a=, b= (+)fi - Q(), R()=a+b (a, b ) (+)fi =( -)Q()+a+b =(+)(-)Q()+a+b =-, = 0=-a+b, fi =a+b a=6, b=6 08 f()+g(), f()-g() ++ Q (), Q () f()+g()=( ++)Q ()+9 f()-g()=( ++)Q ()- + f()=( ++){Q ()+Q ()}+6 Q ()+Q () f()=( ++) + 09 f() ( -)(-) Q(), a +b+c (a, b, c ) f()=( -)(-)Q()+a +b+c f() - + a +b+c - + 0

15 0 ~ 05 f()=( -)(-)Q()+a( -)++, f() - f()=a+7= a=- -( -)++= f()={-;@;}q()+r f()=(-);!; Q()+R ;!;Q(), R 00 + fi +fi + - Q(), a +b+c (a, b, c ) + fi +fi + =( -)Q()+a +b+c =(-)(+)Q()+a +b+c =0, =, =- c=0, a+b+c=5, a-b+c=-5 a=0, b=5, c=0 5 0 f() (-)(-)(-) Q(), R()=a +b+c (a, b, c ) f()=(-)(-)(-)q()+a +b+c f() (-)(-) a +b+c=a(-)(-) f()=(-)(-)(-)q() +a(-)(-), f() (-)(-) Q'() - f()=(-)(-)q'()+-, f()= f()=a= a=;!; R()=;!;(-)(-) R(0)=;!; (-) (-)= 0 f()=(+)q()+r f()=(+);!; Q()+R ;!;Q(), R 05 f()={+;!;}q()+ f()={+;!;}q()+ f()=(+) ;!;Q()+(+)- f()=(+)[;!;q()+]- ;!;Q()+, - 06 f() -- Q() f()=( --)Q()+- f()=(+)(-)q()+- f(-)=-6 f(-) - f( -)=f(-)=-6 07 f() - Q() f()=(-)q()+r f()=r f(-) - f( -)=f()=r 0 f() + Q(), R()=a +b+c (a, b, c ) f()=( +)Q()+a +b+c a +b+c -+ - R()=a( -+)+- f()=( +)Q()+a( -+)+- f(-)= a-6= a= R()=( -+)+- = -- R()= --= f() -7+ Q() f()=( -7+)Q()++ f()=(-)(-)q()++ f()=9 f() - f( )=f()= f()+g() - 6 f()+g()=6 f()+g()

16 RPM f()+g()=8 - f()= f(-5) - f( -5)=f()= 050 f() - Q() + Q'() f()=(-)q()+ Q()=(+)Q'()- f()=(-){(+)q'()-}+ f()=(-)(+)q'()-+5 f(-)=7 f() + -f(-)=- 7= =(+)Q()++5 Q() - Q() = -+=Q()++5 Q()= R +=(-)Q()+R = R= Q() - Q() = +=(-)Q()+ ( R=) 7=Q()+ Q()=5 5 f()=5+9a+b-= a+b=-0, a=-8, b= a+b=6 f()=0, a, b 0% f()=, a, b 0% a, b 0% a+b 0% f() +-=(-)(+) f()=+a+b+=0 a+b=- f(-)=-8+a-b+=0 a-b=, a=0, b=- 057 f()- + f(-)- (-) =0 f(-)= f()= +k ++7 f(-)=+k-+7= k=- 05 f()=(-)q ()+5 f()=(-)q ()+ Q ()+Q () - Q ()+Q (), = f()=q ()+5=-Q ()+ Q ()+Q ()=- 058 ;!; 0 ;!; ;!; ;!; ;&; + +={-;!;}( ++)+;&; 05 f() + f() +, f(-)=0 f(-)=-8-8-a-a+=0 a=- 055 f()= +a +b- f()=6+a+b-=0 a+b=- + +={-;!;} { ++;!;}+;&; + +=(-){ ++;!;}+;&; ++;!;, ;&; a= 06

17 05 ~ 08 -+b=-9 b=-6 0-8=c c=-8 a-b+c=-(-6)-8=0 060 a +b+c={-;!;}(p+q)+r a +b+c={-;!;} ;!;(p+q)+r a +b+c=(-){;!;p+;!;q}+r a +b+c - ;!;p+;!;q, r a=, b=, c=6, d=5 ab+cd= d c b - - a a=-, b=, c=-, d=- abcd=- 06 a=, b=5, c=5, d= abcd= = =+ (+) -(+) -(+)+6=a +b +c+d =a +b +c+d a=, b=5, c=5, d= abcd= d c - -5 b a 0,,, =0 6=-8a+b-c+d = =-a+b-c+d = =d = 5=a+b+c+d,,, a=, b=5, c=5, d= abcd= d 6 c b a 06 a=-5, b=0, c=9 f()=a +b+c f()=-5 +9 f() - f() f()=-5+9= 065 f()= - +a+5 f(-)=6--a+5= -a+9= a= 066 a(-)(-)+b(-)+c= = c= = b+c= b= =0 a-b+c=0 a= a +b +c =+9+= 067 f()=a(-)(-)(-)+b(-)(-) +c(-)(-)+d(-)(-) d 0, =, f()=d(-)(-) 6d=f() c b a =(-)(a +b+c) --=a +(b-a) +(c-b)-c a=, b-a=0, c-b=-, -c=- 07

18 RPM a=, b=, c= abc= 069 +a-b=k(-+) (-k)+(a+k)-b-k=0, -k=0, a+k=0, -b-k=0 k=;!;, a=-;!;, b=-;!; a+b=-;#; 070 f()= +a +b+ f() + f(-)=-+a-b+=0 a-b= f() - 5 f()=+a+b+=5 a+b=, 07 f()=a f()=a+000 f()=0 a=-000 f()= f(-)= = f() (-)(+) Q(), R()=a+b (a, b ) f()=(-)(+)q()+a+b f()=5, f(-)=- a+b=5 -a+b=-, a=, b= R()=+ R()= +=9 (» {» 9 a=;#;, b=;!; ab=;#; 07 f()={-;!;}q()+r f()=(-);!;q()+r f() - ;!;Q(), R a ++b +p (p ) a=( ++b)(+p) = +(p+) +(p+b)+pb 8=p+, 5=p+b, -a=pb p=5, b=-0, a=50 a+b=0 076 f(-)+g(-)=8 f(-)-g(-)=, f(-)=6, g(-)= +f()g() + -+f(-)g(-)=-+6 = Q(), R()=a+b (a, b ) -=(-)Q()+a+b =0 -=b = 0=a+b, a=, b=- R()=- R(00)=00-= p+q (-)(+) -, + = -+p+q=0 p+q=- =- ---p+q=0 -p+q=, p=-5, q= p-q= f()=(+)q()+5 Q() + Q'() Q()=(+)Q'()- f()=(+){(+)q'()-}+5 f()=(+)(+)q'()-+ f() + f(-)=- (-)+=7 08

19 08 ~ f()- -+ Q() f()-=( -+)Q() f()=(-)(-)q()+ + f(+)=(-)q(+)+ f(+) - g()=f()- g() g(-)=g(-)=g()=0 g() +, +, - g()=(+)(+)(-) f()=(+)(+)(-)+ f(-)=- (-) (-)+= f() () f()=+++=0+0 f() - () R()=a +b+c (a, b, c ) =( - +-)Q()+a +b+c = a+b+c=0 R()0( ) 08 ;!; ;!; - -;!; -;&; -;8(; 08 = =a º+a ª+a ++a +aº =- =a º-a ª+a --a +aº + =(a º+a +a ++a +aº) a º+a +a ++a +aº=, =0 aº= a º+a +a ++a = ;!; ={-;!;}{ - -;&;+;(;}+;8!; =(-){ -;!; -;&;+;8(; }+;8!; -;!; -;&;+;8(;, ;8!; 08 f() - Q(), R()=a+b (a, b ) f()=( -)Q()+a+b f()=(-)(+)q()+a+b =, =- f()=a+b, f(-)=-a+b f() a+b = =- f(-) -a+b a+b=6a-b, -a+b=0 -a+b=0 ;!; - -;&; -;(; -;8!; R(-)=-a+b=0 08 f(-)=f(-)=f()= f() +, +, - a+b+c=;!;+(-)+=;!; ;!; d c - - b a a=, b=, c=-, d=-6 abcd= 087 = 5=B =- -8=9C =0 0=-A+B+C,, 09

20 RPM A=, B=5, C=- A+B+C=7 60% A, B, C 0% A+B+C 0% 088 a+b= b=-a a +b+z=a a +(-a)+z=a a a -(+)a++z=0 7 a =0, +=0, +z=0 =0, =-, z= ++z=0 b=-a a 50%,, z 0% ++z 0% f() (-)(-) Q(), a +b+c (a, b, c ) f()=(-)(-) Q()+a +b+c f() (-) 6+ a +b+c (-) 6+, a +b+c=a(-) +6+ f()=(-)(-) Q()+a(-) +6+, f() - 6 f()=a+7=6 a=- -(-) +6+= f() 50% a 0% 0% 090 =(-)Q()+R = R= Q() Q() = =-Q()+ Q()= - Q() - - R 0% Q() 70% 09 (-) Q() +a +b+=(-) Q() = +a+b+=0 b=-a-5 +a -a-5+=(-) Q() (-){ +(a+)-}=(-) Q() - +(a+)-=(-)q() = +a+-=0 a= b=-7 a-b= z=, --z=, z =-, z=-+5 a(-)+b(-)(-+5)+c(-+5)=0 (a-6b-c) +(-a+9b+5c)-5b=0 a-6b-c=0, -a+9b+5c=0, -5b=0 a=5, b=-, c=0 a+b+c=9 00

21 00 ~ 0 09 fi =( ) fi = 8 fi f()= fi f() + f(-)= Q() fi =(+)Q()+ =8 8 fi =(8+)Q(8)+ fi =9Q(8)+ fi fi - R ++ ++fi =(-)Q()+R = 50=R, Q() + Q(-) = =-Q(-)+50 0=-Q(-)+50 Q(-)= (-)a+(-)=(-)(a+) --+=--(-)=(-)(-) ac-bd-ad+bc=ac-ad-bd+bc =a(c-d)+b(c-d) =(c-d)(a+b) =() + 5+(5) =(+5) 6-8+ =() - + =(-) (+5) (-) = +(+6)+ 6 =(+)(+6) --0= +(-8+5)+(-8) 5 =(-8)(+5) (+)(+6) (-8)(+5) 095 f()=a+b f( )=a +b f( )-b f() =(-)(+) =(+)(-) g()=f( )-b g{-;ab;}=0, g{-;ab;}=[a{-;ab;}+b]-b=0 ;ab;(b-a)=0 ab+0 a-b=0 096 f() + g(), g() - h() f()=(+)g()+5 g()=(-)h()- h()=(+)-=- g()=(-)(-)- g()= -- f()=(+)( --)+5 f()= f() - f()=7-8-5+= =(8) -() =(8+)(8-) a -7b =(a -9b )={(a) -(b) } =(a+b)(a-b) (+) -(-) =(++-){+-(-)}=(+) 00 a +b +c -ab-bc+ca =a +(-b) +c + a (-b)+ (-b) c+ c a =(a-b+c) + ++(++) = =(++) (a-b+c) (++) 00-8= - =(-)( ++) 7-8 =() -() =(-){() + +() } =(-)(9 +6+ ) = =(-) 0

22 RPM = + + () +() =(+) (-) 005 a -b +c +abc =a +(-b) +c - a (-b) c =(a-b+c)(a +b +c +ab+bc-ca) + -+ = =(++)( ) 006 a +a +=a +a + =(a +a+)(a -a+) (+) + +6 = + () +() =( ++ )( -+ ) 007 +=t (+) -(+)+=t -t+=(t-)(t-) =(+-)(+-) =(-) +5=t ( +5+)( +5+)- =(t+)(t+)- =t +6t-6=(t+8)(t-) =( +5+8)( +5-) +=X, -=Y (+) +(+)(-)-(-) =X +XY-Y =(X-Y)(X+Y) ={(+)-(-)}(++-) =(+5)(-)=(+5)(-) 008 =t +5-6=t +5t-6 =(t-)(t+6)=( -)( +6) =(+)(-)( +6) +9 +5=( +0 +5)- =( +5) - =( ++5)( -+5) +-a -a=(-a)+ -a =(-a)+(+a)(-a) =(-a)(++a) 00 f()= f()= f()=(-)( --6) f()=(-)(+)(-) f()= f(-)=0, f()= f()=(+)(-)( -+) 0 a +a =a(+) 0 ab-cd-ac+bd=ab-ac-cd+bd =a(b-c)+d(b-c) =(a+d)(b-c) (-)-(-)+(-)z =(-)+(-)+(-)z =(-)(+z+) 0 + -z-z=(+)-z(+) =(+)(-z) 0 (-) +(-)=(-) -(-) =(-)(--) =(-)(-) a=-, b=- a=-, b=- ab= = -(+)+ ++ = -(+)+(+)(+) ={-(+)}{-(+)} =(--)(--) 05 - = -() =(+)(-) afi b-abfi =ab(a -b ) =ab{(a ) -(b ) } =ab(a +b )(a -b ) =ab(a +b )(a+b)(a-b) 0

23 0 ~ 06 (a-b) -(c-d) ={(a-b)+(c-d)}{(a-b)-(c-d)} =(a-b+c-d)(a-b-c+d) a -8b =a -(b) =(a-b)(a +ab+b ) +7= + =(+)( -+9) - =( ) -( ) =( + )( - ) =( + ){( ) -( ) } =( + )( + )( - ) =( + )( + )(+)(-) 0 +=t 6(+) +(+)z-z =6t +tz-z =(t-z)(t+z) =(+-z)(++z) 0 a -ab+b -9c =(a -ab+b )-9c =(a-b) -(c) =(a-b+c)(a-b-c) =a-b+c = - -(-) =(+)(-)-(-) =(-)(+-) 06 a +6=a + =(a+)(a -a+6) 07 (a-b) -5b =(a-b) -(5b) =(a-b-5b){(a-b) +(a-b) 5b+(5b) } =(a-7b)(a -ab+b +5ab-0b +5b ) =(a-7b)(a +ab+9b ) 08 fl -fl =( ) -( ) =( + )( - ) =(+)( -+ )(-)( ++ ) 09 -=X, -=Y (-) -(-)(-)-(-) =X -XY-Y =(X+Y)(X-Y) ={(-)+(-)}{(-)-(-)} =(-6) =(-) 00 -(a+)+(a+)(a+) ={-(a+)}{-(a+)} =(-a-)(-a-) (-a-)+(-a-)=-a-=+, -a-= a=- 0 +5=t (+5) -(+5)+=t -t+ =(t-)(t-) =(+5-)(+5-) =(+)(+) a=, b= a=, b= a+b=7 (-) = -( -+) =( ) -(-) =( +-)( -+) =(+)(-)( -+) - -- =-( ++ ) =-(+) =(++)(--) a b+b c-b -a c=a (b-c)-b (b-c) =(b-c)(a -b ) =(b-c)(a+b)(a-b) 06 a +a c -b c -b =(a -b )+c (a -b ) =(a +b )(a -b )+c (a -b ) =(a -b )(a +b +c ) =(a+b)(a-b)(a +b +c ) =( +6 +9)- =( +) - =( ++)( -+) A=-, B= AB=- 08 =t -5 +=t -5t+ =(t-)(t-)=( -)( -) =(+)(-)(+)(-) =a, =b =a -0ab+9b =(a-b)(a-9b) =( - )( -9 ) =(+)(-)(+)(-) 0

24 RPM =a, =b -7 - =a -7ab-b =(a+b)(a-b) =( + )( - ) =( + )(+)(-) (-)(-)(-)(-)+ ={(-)(-)}{(-)(-)}+ =( -5+)( -5+6)+ =(X+)(X+6)+ -5=X =X +0X+5=(X+5) =( -5+5) 09 a +=(a +a +)-a =(a +) -(a) =(a +a+)(a -a+) =( - + ) =( - ) -() -6 + =( +- )( -- ) 0 (-)(-)(+)(+)+ ={(-)(+)}{(-)(+)}+ =( +-)( +-)+ =(t-)(t-)+ +=t =t -t+8=(t-6)(t-8) =( +-6)( +-8) =(+)(-)( +-8) a+b+c=-7 0 a -a=t (a -a-5)(a -a+)+8 =(t-5)(t+)+8 =t -t- =(t-)(t+) =(a -a-)(a -a+) =(a -a-)(a-)(a-) 0 -=X ( -+)( --)+5 =(X+)(X-)+5 =X -X- =(X-)(X+) =( --)( -+) =(-)(+)(-) -=X ( -) =( -) +( -)-5 =X +X-5 =(X+5)(X-) =( -+5)( --) =( -+5)(-)(+) 0 (+) (-)(+7)+ =( ++)( +-)+ =(X+)(X-)+ +=X =X -7X+60=(X-5)(X-) =( +-5)( +-) =(+5)(-)(+6)(-) a+b+c+d= = +(+)-( -5+) = +(+)-(-)(-) ={+(-)}{-(-)} =(+-)(-+) 06 b a b-a c+bc-ac =(a +c)b-a c-ac =(a +c)b-ac(a +c) =(a +c)(b-ac) 07 a a +5-a-a-0 =( --)a+5-0 =(-)(+)a+5(-) =(-){a(+)+5} =(-)(a+a+5) = +(5+)+( ++) = +(5+)+(+)(+) =(++)(++) a=, b=, c= a+b+c= = +(-)-( -) = +(-)-(+)(-) ={+(-)}{-(+)} =(+-)(--) 0

25 06 ~ (+)(-)++5- =( +-)++5- = +(+)- +5- = +(+)-(-)(-) ={-(-)}{+(-)} =(-+)(+-) =( +) +( ++)++ =(+) +( ++)++ ={+(+)}{(+)+} =(++)(++) a+8- = -(-a)-(6-8+) = -(-a)-( -+) = -(-a)-(-)(-), (-)-(-)=-(-a) --=-+a a=- - 0 a a (b+c)+b (c+a)+c (a+b)+abc =a b+a c+b c+b a+c a+c b+abc =(b+c)a +(b +c +bc)a+b c+bc =(b+c)a +(b+c) a+bc(b+c) =(b+c){a +(b+c)a+bc} =(b+c)(a+b)(a+c) =(a+b)(b+c)(c+a) =(b-c)a -(b+c)(b-c)a+bc(b-c) =(b-c){a -(b+c)a+bc} =(b-c)(a-b)(a-c) =-(a-b)(b-c)(c-a) -(a-b)(b-c)(c-a) ()= =- - (a-b)(b-c)(c-a) 06 a a(b+c) +b(c+a) +c(a+b) -abc =a(b +bc+c )+b(c +ac+a )+c(a +ab+b )-abc =ab +abc+ac +bc +abc+a b+a c+abc+cb -abc =(b+c)a +(b +bc+c )a+b c+bc =(b+c)a +(b+c) a+bc(b+c) =(b+c){a +(b+c)a+bc} =(b+c)(a+b)(a+c) =(a+b)(b+c)(c+a) (a+b)(b+c)(c+a) = { +5-+;[%;+ } = { + +5+;[%;-} = [{+;[!;}+5{+;[!;}-6] +;[!;=t {+;[!;}+5{+;[!;}-6 =t +5t-6=(t+6)(t-) ={+;[!;+6}{+;[!;-} ()= {+;[!;+6}{+;[!;-} ()={+;[!;+6} {+;[!;-} ()=( +6+)( -+) 0 a (b-a)c +(c-b)a +(a-c)b =bc -ac +ca -ba +ab -cb =(c-b)a -(c -b )a+bc -cb =(c-b)a -(c+b)(c-b)a+bc(c-b) =(c-b){a -(c+b)a+bc} =(c-b)(a-b)(a-c) =(a-b)(b-c)(c-a) 05 ab(a-b)+bc(b-c)+ca(c-a) =a b-ab +b c-bc +c a-ca =(b-c)a -(b -c )a+b c-bc = { ---;[#;+ } = [ + -{+;[!;}-] = [{+;[!;}-{+;[!;}-] +;[!;=t {+;[!;}-{+;[!;}- =t -t-=(t+)(t-) ={+;[!;+}{+;[!;-} 05

26 RPM ()= {+;[!;+}{+;[!;-} ()={+;[!;+} {+;[!;-} ()=( ++)( -+) = { +-8+;[#;+ } = [ + +{+;[!;}-8] = [{+;[!;}+{+;[!;}-0] +;[!;=t {+;[!;}+{+;[!;}-0 =t +t-0=(t+5)(t-) ={+;[!;+5}{+;[!;-} 05 b -ba-c +ca=(c-b)a+b -c =(c-b)a+(b-c)(b+c) =(c-b)a-(c-b)(b+c) =(c-b){a-(b+c)} =(c-b)(a-b-c)=0 a, b, c a<b+c, a-b-c+0 c-b=0 b=c b=c b=c 50% a, b, c 0% 0% ()= {+;[!;+5}{+;[!;-} ()=( +5+)( -+) ()=( +5+)(-) a=5, b=, c= abc= A+B =( - -)+( + ++) = = = { ++5+;[$;+ } = [ + +{+;[!;}+5] = [{+;[!;}+{+;[!;}+] = {+;[!;+}{+;[!;+} =( ++)( ++) 05 a +b +c -abc =(a+b+c)(a +b +c -ab-bc-ca) =;!;(a+b+c){(a-b) +(b-c) +(c-a) }=0 a+b+c>0 (a-b) +(b-c) +(c-a) =0 a-b=0, b-c=0, c-a=0 a=b=c 05 a +a b-ac +ab +b -bc =-(a+b)c +a +a b+ab +b =-(a+b)c +a (a+b)+b (a+b) =(a+b)(-c +a +b )=0 a, b, c a+b>0 -c +a +b =0 a +b =c c 05 ab(a+b)-bc(b+c)+ca(a-c) =a b+ab -b c-bc +ca -c a =(b+c)a +(b -c )a-b c-bc =(b+c)a +(b+c)(b-c)a-bc(b+c) =(b+c){a +(b-c)a-bc} =(b+c)(a-c)(a+b)=0 a+b>0, b+c>0 a-c=0 a=c a=c a -ac+c = a -a +a =, a = a=c= ( a>0) a +c = + = f() + f(-)=a-6=0 a= f()= f()=(+)( ++)

27 08 ~ f()= - +- f()= f()=(-)( -+) f()= + +- f{;!;}=0 f()={-;!;}( ++) =;!;(-) ( ++) =(-)( ++) f()= f{-;!;}=0 -;!; ;; ;; -0-0 f()={+;!;}( -0+) =(+)( -5+6) =(+)(-)(-) f()= f()=0, f(-)= f()=(-)(+)( +-) =(-)(+)(-)(+) 057 f()= f(-)= f()=(+)( --) =(+)(+)(-) a +b +c = + +(-) =6 ;!; - ;; - ;; -0 80% a +b +c 0% f()= f()=0, f()= f()=(-)(-)( +-) =(-) (-)(+) =a _ _00+5 a -5 a -5 = _ (a-5) a +5a+5 (a-5)(a+5) (a-5)(a +5a+5 ) = _ 5 (a-5) a +5a+5 a+5 = _(a-5)=a+5 a-5 =00+5= =(0-)(0+)+(-6)(+6) +(8-0)(8+0) =-_-_50-_58 =-(+50+58) =-_50= = = f()= f()= f()=(-)( +6+9) =(-)(+) =(97-)(97+) =95 00 = = = ( ++)( -+) = -+ = ++ =(+) - =0-9 a=

28 RPM 06 f()=0, f(-)= f()=(-)(+)( -+) =(-) (+) f()=(-) (+) =000_ = [, ]+[7, 5]+[, 9]+[5, ] =( - )+(7-5 )+( -9 )+(5 - ) =(-)(+)+(7-5)(7+5)+(-9)(+9) +(5-)(5+) =_+_+_0+_8 =(++0+8) =_6= = 99 _0 (-) (+) = 9998_0000+ ( -) + ( -) ( -) = = - + ( -) = -=00 -= = 5_7+5 =(+)(+)(+6)+5 ={(+6)}{(+)(+)}+5 =( +6)( +6+8)+5 =A(A+8)+5 +6=A =A +8A+5=(A+)(A+5) =( +6+)( +6+5) =( +6+)( +6++) =n(n+) n= +6+= +6_+= (a+b+c)=0 a+b+c=0 a +b +c -abc =(a+b+c)(a +b +c -ab-bc-ca)=0 069 =+', =-' +=, -=', = = (-)- (-) =(-)( - ) =(-)(-)( ++ ) =(-) ( ++ ) =(-) {(+) -} =(') ( -) = (a+b+c)(bc+ca+ab)-abc =abc+ca +a b+b c+abc+ab +bc +c a+abc-abc =(b+c)a +(b +bc+c )a+b c+bc =(b+c)a +(b+c) a+bc(b+c) =(b+c){a +(b+c)a+bc} =(b+c)(a+b)(a+c) = =6 0% 0% 0% 07 [a, b, c]+[b, c, a]+[c, a, b] =a (b-c)+b (c-a)+c (a-b) =(b-c)a -(b -c )a+bc(b-c) =(b-c)a -(b+c)(b-c)a+bc(b-c) =(b-c){a -(b+c)a+bc} =(b-c)(a-b)(a-c) =-(a-b)(b-c)(c-a) a +b +a b+ab =(a +a b)+(b +ab ) a +b +a b+ab =a (a+b)+b (a+b) a +b +a b+ab =(a+b)(a +b ) a +b +a b+ab =(a+b){(a+b) -ab} a +b +a b+ab = ( - )=5 068 a+b=-', b+c=-+', c+a=--' 07 [,, z]+[, z, ]+[z,, ] = +z+ +z+z + = + +z ++z+z =(++z), +=7, +z=- (++z)= ++z= ()= = 08

29 00 ~ 0 07 [a, b, c]+[b, c, -a] =(a+b)(b+c)+(b+c)(c-a) =(b+c){(a+b)+(c-a)} =(b+c)(c+b) =[b, c, b] ( [c, b, c]) 07 ( +) ( -)-7 =( +) +( -) -( +)( -)-7 = ( - + -)-7 = -9 +6=( - +) =( -)( -) =(+)(-)( -) (+)(-)( -) =() -(6) =(+6)(-6) =(+)(-) -6=( ) - =( +)( -) =( +)(+)(-) -5-=(-)(+) +8=(+)( -+) - +z-z = -( -z+z ) = -(-z) =(+-z)(-+z) 076 a -a c-ab +b c =a (a-c)-b (a-c) =(a-c)(a -b ) =(a-c)(a+b)(a-b) 077 +=X ( +) =X +X-6 =(X+)(X-) =( ++)( +-) =( ++)(+)(-) 078 (+)(+)(+)- ={(+)}{(+)(+)}- =( +)( ++)- +=t =t(t+)- =t +t- =(t-)(t+6) =( +-)( ++6) =(-)(+)( ++6) 079 (-) +(+) =(-) +(+) -(+--) =(-) -{(+)-(+)}+(+) =(-) -(-)(+)+(+) -=X, +=Y ()=X -XY+Y =(X-Y)(X-Y) ={(-)-(+)}{(-)-(+)} =(--)(--6) =( ) -( ) =( - )(fl + +fl ) =(-)( ++ )(fl + +fl ) = =( +) - =( ++)( -+) = ( ++)-9 = (+) -9 =( +) - =( ++)( +-) f()= - +- f()=0, f(-)= f()=(-)(+)( -+) 08 +a +b (-) 0 a 0 b+b a+ a++b a+ a+ a++b a+ a+ a+ a+=0, a++b=0 a=-, b= - +=(-) ( ++) =(-) (+) (-) (+) 08 f()= +(a-) +(-a)+a f()=0 09

30 RPM a- -a -a a- -a a- -a -0 f()=(-){ +(a-)-a} =(-)(-)(+a) +(a-)-a=(-)(+a) =( ) +8 +( ) - =( + ) -() =( ++ )( -+ ) p+q=0 086 [, -, ]+[-,, ] =(+)(-)+(--)(--) =(+)(-)-(+)(-) =(+){(-)+} =(+)(+)=(+) = +-( -+) = +-(-)(-) ={-(-)}{+(-)} =(-+)(+-) = +(-)+ -- = +(-)+(+)(-) =(++)(+-) (++)+(+-)= =(+) -(+)+6-8 =(+) -(+-)-8 =t -(t-)-8 +=t =t -8-(t-) =(t-)(t +t+)-(t-) =(t-)(t +t+-) =(+-){(+) +(+)+-} =(+-)( ) = + +(-) - (-) =(+-)( ) 090 (-)+(-z)+(z-)=0 (-) +(-z) +(z-) =(-)(-z)(z-) (+) a +b +c -abc =(a+b+c)(a +b +c -ab-bc-ca) a+b+c=0 a +b +c =abc 09 f(a, b, c)+f(b, c, a)+f(c, a, b) =a (b-c)+b (c-a)+c (a-b) =(b-c)a +(c -b )a+b c-bc =(b-c)a +(c-b)(c+b)a+bc(b-c) =(b-c){a -(c+b)a+bc} =(b-c)(a-b)(a-c) z+ z =( - )z+( - )+( - ) =(-)(+)z+(-)( ++ )+(-) =(-){-(+)z+( ++ )+} =(-){-(+)z+( ++ )} =(-){-(+)z+(+) } =(-){(+)(-z++)} =(-)(+)(+-z) 09 (a+b+c) =a +b +c +(ab+bc+ca) =+(ab+bc+ca) ab+bc+ca= a +b +c -abc =(a+b+c)(a +b +c -ab-bc-ca) a +b +c - = (-) a +b +c = a +b +c =(a+b+c) -(ab+bc+ca) 8= -(ab+bc+ca) ab+bc+ca= a +b +c - abc a +b +c -abc = abc (a+b+c)(a +b +c -ab-bc-ca) = abc (8-) = =8 095 a(b -c )+b(c -a )+c(a -b ) =ab -ac +bc -ba +ca -cb =(c-b)a +(b -c )a+bc -cb =(c-b)a +(b-c)(b+c)a+bc(c-b) =(c-b){a -(b+c)a+bc} =(c-b)(a-b)(a-c) =(a-b)(b-c)(c-a)=0 a-b=0 b-c=0 c-a=0 a=b b=c c=a ABC 00

31 0 ~ G()= +a +b -- G() -, + G()=+a+b--=0 a+b=7 G(-)=6-8a+b+8-=0 a-b=5 a=, b= G()=(-)(+)( ++) f()= ++ G()= +a +b G() (-)(+) - a b a+ a+b+ a+b- - a+ a+b+ a+b- a+b a+ a-b-6 - a- -a+b+ a-b-9 a+b-7=0, a-b-9=0 a=, b= f()= +(a-)+(-a+b+) = = + =(+)(+)(+)+ ={(+)}{(+)(+)}+ =( +)( ++)+ +=X ()=X(X+)+ ()=X +X+=(X+) ()=( ++) ()=( +_+) ()=55 'ƒ_ƒ_ƒ_ƒ+="ç55 =55 55 = 0% 0% +=X 0% 0% =(7+9)(7-9)+(+)(-)+(5+7)(5-7) =-(6++)= =(+9)(-9)+(7+5)(7-5)+(+)(-) =(0++)=7 - = =- 7-0% 0% 0% 099 (-)(-)(+)(+)+k ={(-)(+)}{(-)(+)}+k =( +-)( +-)+k =(X-)(X-)+k +=X =X -X++k =X -X+9-9++k =(X-7) -5+k =( +-7) -5+k -5+k=0 k=5 5 0% 0% k 0% 000 (a-b)c -(a -b )c +(a -b )(a+b) =(a-b)c -(a-b)(a +ab+b )c +(a -b )(a +b )(a+b) 0

32 RPM =(a-b)c -(a-b)(a +ab+b )c +(a+b) (a-b)(a +b ) =(a-b){c -(a +ab+b )c +(a+b) (a +b )} =(a-b){c -(a+b) }{c -(a +b )}=0 a, b, c a+b>c c -(a+b) +0 a-b=0 c -(a +b )=0 a=b c =a +b a=b c a=b c c 0% 0% 0% = +(+a)-( ++) = +(+a)-(+), (+) + -(+) a=(+)-(+) =+ a= 00 +z= z= z =- - -(-) = =(--+) =(-)(-) =(-z)(-)(-) =(-)(-)(-z) (-)(-)(-z) 00 00=, 999= = = - = _00 =999 +(00+999)_00 = +(+) = ++ - (-)( ++ ) = = =- =00-999= 00 a+b+c=0 a+b=-c, b+c=-a, c+a=-b a +b +c -abc =(a+b+c)(a +b +c -ab-bc-ca)=0 a +b +c =abc a{ + }+b{ + }+c{ + } b c c a a b a(b+c) b(c+a) c(a+b) = + + bc ca ab a (b+c)+b (c+a)+c (a+b) = abc -a -b -c -(a +b +c ) = = abc abc abc =- =- - abc a A (a+) -, B (a+) - {(a+) -}-{(a+) -} =(a+) -(a+) =(a++a+)(a+-a-) =(a++)(-) 006 a +b +c -abc =(a+b+c)(a +b +c -ab-bc-ca) =;!;(a+b+c)(a +b +c -ab-bc-ca) =;!;(a+b+c){(a -ab+b )+(b -bc+c ) +(c -ca+a )} =;!;(a+b+c){(a-b) +(b-c) +(c-a) }=0 a, b, c a+b+c>0 (a-b) +(b-c) +(c-a) =0 a=b=c, 6 a+b+c=a=6 a= ' _ =' ' a ' a 0

33 0 06 (+i)(-i)=-6i+i-8i (+i)(-i)=-i-8 (-) (+i)(-i)=-i 05 ~ ' -5='5i ' -6='ß6i=i ' -7='ß7i='i -' -=-'ßi=-'i '5i i 'i -'i 5-i +i 07 5 = (5-i)(-i) (+i)(-i) 5-5i-i+i = -i -8i = =-i 008 ' -= i ' -8= '8i= 'i ' -6= 'ß6i= 6i i 'i 6i =(+i) +(+i)(-i)-(-i) +- =(+i)+(+)-(-i) +- =5+8i 009 a+bi b=0, b+0, a=0, b+0 'i =- (,,, i =- {,,, 9, 00 +(-)i=6-i =6, -=- =, =0 0 (+)+(-)i=+i +=, -= =, = 0 -+(+)i=+i -=, += =, = i =-5-7i +i =-i -i =+i i+ =-i i =-i = 0 (5+i)+(-+6i)=(5-)+(+6)i (5+i)+(-+6i)=+9i 05 (7+i)-(-i)=(7-)+(+)i (7+i)-(-i)=+5i -i++i 09 ;[!;+;]!;= + = +i -i (+i)(-i) ;[!;+;]!;= 5 =;5$; -i 00 i fi =(i )fl i=i (-i)fi =-ifi =-i i=-i -i =-i i =-(-i)=i i +i =(i ) fi +(i )fi =+= i -i i 0 ' - ' -8='i_'8i='ß6i =- 'ß 'ß 'ßi 0 5 = = =-'i=-i ' - 'i 'i ' -6 'ß6i 0 5 = ='= ' - 'i '8 ' 0 ' - ' -6-5 ='i_'6i- ' -6 i ' - ' -6- 'i ='ß8i - i ' - ' -6- ' =-'+ i 05 a+bi a=0, b+0 i, i =-i, ifi =i i=i 06 0=0+0 i a=0, b=0-5i -9 ' -9= i, 0

34 RPM 07 a+bi b=0, 0 +' -=+i i +=-+=0-5i -5 6, i + 08 i+i =i-i=0 i+ifi =i+i i=i+i=i ('i) =i =-, 09 a+b=(+i)+(-i)= ab=(+i)(-i)= b a a +b (a+b) -ab + = = a b ab ab - = =0 00 i - =- + i =--i 0 (+'i) +(-'i) =(+'i+i )+(-'i+i ) =+'i+-'i = -'i +'i 0 + +'i -'i (-'i) +(+'i) = (+'i)(-'i) (9-'i+8i )+(9+'i+8i ) = 9-8i = 7 5(+i) 0 = =+i (-i)(+i) 5(-i) = =-i (+i)(-i) +=, =5 + =(+) - = - 5=-6 0 a+b=(+i)+(-i)=+i ab=(+i)(-i)=+i a b+ab =ab(a+b) =(+i)(+i)=9+i a=9, b= a+b= -i -+i 05 -i+ -i+ -i +i (-i)(+i) (-+i)(-i) =-5i+ + (-i)(+i) (+i)(-i) -i +i =-5i+ + =-5i++i=6-i a=6, b=- a+b= 06 (+i)z=5-i 5-i (5-i)(-i) z= = = +i (+i)(-i) -6i z= =-i a=, b=- a +b = +(-) =-9 07 (+i)+(-i)=5-i +i+-i=5-i (+)+(-)i=5-i +=5, -=- =, = += 08 (+i) =+i+i =+i (-i) =-i+i =-i (+i) +(-i) =(+i)+(-i) (-i) +(-i) =(+)+(-)i (-i) +(-i) =-9-i 5-5i-i+i -i (+)=-9, (-)=-, +=-, -=- =-, =- (+i)(+i) =(+i)(-i) =-i+i+ =(+)+(-)i =-i -9 z 50% a, b 0% a +b 0% 0

35 050 ~ 05 +=, -=- 9 =, = =-, =- =, = z=a+bi (a, b ) z =a-bi z+z = (a+bi)+(a-bi)=a= a= zz = (a+bi)(a-bi)=a +b =, b =0 b=0 z= (+i)+(-i) 09 + = -i +i (-i)(+i) + - = + i =0-7i + - =0, =-7, +=0, -=- =, =7 -=- - -i 00 (+i)+ =-i -i -i (+i)(-i)+-i=(-i)(-i) 5+-i=--8i 5+=-, -=-8 =-, =8 5 5+=5 {- }+8= z=a+bi (a, b ) z =a-bi (+i)z +(-i)z= (+i)(a-bi)+(-i)(a+bi)= a-bi+ai+b+a+bi-ai+b= a+b= a+b= a+b=, 0 z=a+bi (a, b ) z =a-bi zz =7 (a+bi)(a-bi)=7 a +b =7 zz =7 z =;z&; z+;z&;=z+z =, (a+bi)+(a-bi)=, a= a= a= +b =7, b = b= ' z ' ' z=a+bi zz =7 0% z+z = 0% a 0% z 0% -i 50%, 0% 5+ 0% 0 z=a+bi (a, b ) z =a-bi (+i)z+z =0-i (+i)(a+bi)+(a-bi)=0-i (a+bi+ai-b)+(a-bi)=0-i (a-b)+(a-b)i=0-i a-b=0, a-b=- a=, b= z=+i 05 aa -a b-ab +bb =a(a -b )-b(a -b ) =(a-b)(a -b ) =(a-b)(a-b) a=5-i, b=-i a-b=(5-i)-(-i)=-i a-b =+i ()=(-i)(+i)= -i =5 06 z=+i z =-i z -i +i (-i) +(+i) 5 z + 5= + = z z +i -i (+i)(-i) --i-+i + = =-;5^; 5 05

36 RPM z=-i z =+i z+z =, zz =(-i)(+i)= z- z - z (z-)+z(z -) + = z z zz zz -(z+z ) = zz - = = -;5^; (-)(-) =0 (-)(-)=0 = =, = 05 (+i)(-i)=(+)+(-)i +=0, -+0 =-;!; 07 aa +a b+ab +bb =a (a+b)+b (a+b)=(a+b)(a +b ) =(a+b)(a+b) =(+5i)(+5i) =(+5i)(-5i) =6+5= 08 a=a+bi (a, b ) a =a-bi a=a b=-b b=0 a=a ( ) aa =0 (a+bi)(a-bi)=0 a +b =0 a=b=0 a=0( ) (a-i)(b+i) =(a -i) (b +i) (a-i)(b+i) =(a +i) (b -i) (a-i)(b+i) =a b -a i+b i+ (a-i)(b+i) =a b -(a -b )i+ (), 09 i(+i) =i( +i+i ) i(+i) =i( +i-) i(+i) =-+( -)i -=0 = ( -7+)+(-)i -7+=0, =0 (-)(-)=0 = = -+0 +, = 05 (i+) -(i+5)+(6+i) = i+ -i-5+6+i =( -5+6)+( -+)i , -+=0 z=a+bi (a, b ) z =(a+bi) =(a -b )+abi z a -b <0 ab=0 a=0 b=0 a=0,-b <0 b+0 z <0 b=0,a <0 a=0, b+0 --'i 05 = =--'i, +=-'i ++=- ++= = ( ++)+= +i +i 05 z= = = -i (-i)(+i) z=+i, z-=i z -z+=- z =z- z -z+=(z-)-z+ z -z+=-z+ +i z -z+=(-)_ + z -z+=-(+i)+ z -z+=-i -i -i 055 z= = (-i)(+i) 5 (-i)(+i) +i = =+i z-=i z -z+=- z -z+5=0 z -z +5z+=z(z -z+5)+= 06

37 05 ~ =-i -=-i -+=-( ) -= = ( -+) = (-+) = =-+=- ( ) -+= = ( -+)+( -+)-=- 057 n i «=, i «± =i, i «± =-, i «± =-i i+i +i +i ++i =(i+i +i +i )++(i +i +i +i )+i +i =(i--i+)++(i--i+)+i- =i = -- +=0 i i i i i i i i i i i =+{ }++{ } i i i i i i i i =+{ -- +}++{ -- +} i i i i = 059 i+i +i ++9i +50ifi =(i--i+)++(5i-6-7i+8)+9i-50 =(-i)++(-i)+9i-50 =(-i)+9i-50=-6+5i =-6, =5 +=- - +i (+i) i 060 z= = = =i -i (-i)(+i) z+z +z +z =i+i +i +i =i--i+=0 +z+z +z +z +zfi ++z =+(z+z +z +z )++(z +z +z +z ) =+(i--i+)++(i--i+) = +i -i { } { } i +i =i -(-i) =(i ) i -{(-i) } (-i) =i -(-i) =i =-i -i 06 z= ' -i -i z ={ } = =-i ' z =(z ) =(-i) =- z =(z ) =(-) = -i { }n= n 8 ' 8 z z 0% z«= z«0% n 0% -i (-i) -i 06 = 5 = =-i +i (+i)(-i) +i (+i) i = 5 = =i -i (-i)(+i) -i { } n+ +i -{ } n+ +i -i =(-i) «± -i «± =(-i) «(-i)-i «i =-i-i ( (-i) =, i =) =-i+i=0 n +i { } «+i =[{ } ] «' ' +i- ={ } «=i«-i { } «-i =[{ } ] «' ' -i- ={ } «=(-i)«=-i«+i { } «-i +{ } «=i«+(-i«)=0 0 0 ' ' +i (+i) i 06 = = =i -i (-i)(+i) -i (-i) -i = = =-i +i (+i)(-i) -i (-i) -i 06 = 5 = =-i +i (+i)(-i) +i (+i) i = 5 = =i -i (-i)(+i) 07

38 RPM -i +i f{ }+f{ }=f(-i)+f(i) +i -i -i +i ={ } 0 0 +{ } 0 0 +i -i =(-i) +i ={(-i) }fi (-i) +(i )fi i =--=- 065 ' -'='i '='6i=' -6 ' -' -='i 'i=-'6 ' - 'i 5= =Æ;@;i=Æ -;@; ' ' ' - 'i 5= =Æ;@; ' - 'i ' ' 'i 5= = 5=-Æ;@;i=-Æ -;@; ' - 'i 'i 066 a<0, b<0, 'a'b=-' ab " (-)(-)+' -' - 'ß7 067 ('+' -)('-' -)+' -' -7+ ' - ' =('+'i)('-'i)+'i_'i+ 5 'i =6-i+6i+-9-i=0 -' - +' ' - -' -6 -i +i -i +i = 5+ 5= + +i -i +i -i (-i) +(+i) -i+i = = =0 0 0 (+i)(-i) 068 0<a< a-<0 ' -a a- 'a_' -a+' a-_' -a+ 5 _æ ' a- -a ' -a -a ='a_'ai+' -ai_' -a+ _æ - ' -ai -a =ai+(-a)i+ _i=+i +i i 'a 069 =-Æ;bA; a>0, b<0 'b " (a-b) - a +" b = a-b - a + b " (a-b) - a +" b =a-b-a-b " (a-b) - a +" b =-a-b - ' -a -a 07 =-æ 5 'ƒ-a -a -a=0 -a>0, -a<0 <a a->0, a- 0 a- + a- =(a-)-(a-)= 07 'a'b=-' ab a<0, b<0 "çab = b 'a=-b'a ( ) 'b =æ;ab; () 'a a >0, b >0 " a " b ="ça b =" (ab) = ab ab>0 ab =ab () a+b<0 a+b =-a-b a + b =-a-b ( ), 07 ' -'5='i '5='ß0i=' -0 ' -' -='i 'i=i =- ' - 'i 5= =Æ;@;i=Æ -;@; ' ' ' - 'i 5= =Æ;8@;=Æ;!;=;!; ' -8 '8i ' ' 'i 5= = 5=-Æ -;5#; ' -5 '5i -'5 '8 ' - 07 ' -å'+' -å' -å ' - ' - '8 ' i ='i_'+'i_'8i+ + 'i 'i =i--i+ =- 075 i =-, i =-i, i = i +i + + i i =(i ) i +(i ) i + + (i ) (i ) i =i +i ++ i =--i+-i=-i 070 'ƒ- -å'ƒ-=-" =-" (- - )( -) --=0 -=0 --<0, -<0 076 (+i)+(5-i)=(+5)+(-)i (+i) +(5-i) =5-i +5-(-)i=5-i 08

39 05 ~ =5, -= =5, =- -=7 (-i)+(+i) = +i -i (+i)(-i) ++(-+)i = = + i=-i =, =- 5 5, +=5, -+=-5 =0, =5 +=5 +'i -'i 078 += + = +'i -'i + = = = + (+) - + = = =-=- 079 (+i) =i, (-i) =-i (+i) (+i) (-i) {(+i) }fi (-i) = = (-i) (-i) (-i) {(-i) }fi (i)fi (-i) = =-i (-i)fi 080 z=-i z =+i -z - -z i i = + z z +i -i i(-i)+i(+i) i = = =i (+i)(-i) 08 z=a+bi z =a-bi z+z = a= a= zz = a +b = a= +b =, b = b=' ( b>0) z=+'i 08 b=+bi b =-bi a+b =a-i+-bi a+b =(a+)-(+b)i a+b =5-i +'i a+=5, +b= a=, b= a+b= 08 z# i=z+i-zi=(-i)z+i (-i)z+i=+i, (-i)z=+i +i (+i)(+i) z= = -i (-i)(+i) +6i z= =+i +i +i a-i (+i)(-i)+(a-i)(+i) 08 z= + = +i -i (+i)(-i) -i+a+ai-i+ = a+5 a- = + i a+5 a- z = - i a- a- z=z =- a-=0 a= 'ƒ =-æ 5 'ƒ- - -=0 ->0, -<0 æ =--(-)+- =- 086 aa +a b+ab +bb =a (a+b)+b (a+b) aa -a b-ab +bb =(a+b)(a +b ) aa -a b-ab +bb =(a+b)(a+b) a=+i, b=-+i a+b=(+i)+(-+i)=-+i a+b =--i ()=(-+i)(--i) ()=(-) -(i) =7 087 z=(+i)a +(+i)a+(i-) z=(a +a-6)+(a +a+)i z a +a-6=0, a +a++0 a +a-6=0 (a+)(a-)=0 a=- a=;#; a +a++0 (a+) +0 a+-, a=;#; 09

40 RPM +i (+i) i 088 5= 5 = =i -i (-i)(+i) +i f{ 5}=f(i)=ifi + =(i ) i i ifi (i ) i f{ }=i + =- i 089 { 5} 8n +{ 5} 8n +i =[{ } ] n -i 5 +[{ 5} ] n ' ' +i+i ={ } n -i+i +{ } n =i «+(-i) «=+= 090 i+i +i +i =i--i+=-i 5ifi +6ifl +7i +8i =5i-6-7i+8=-i +i ' -i ' 97i +98i +99i +00i =97i-98-99i+00=-i i+i +i ++00i =(-i)_5 =50-50i =50, =-50 +=0 -'i 09 = =-'i, -=-'i -+=- -+= = ( -+)+( -+)+ = 09 a b=- ab =(a b) =(-) =- a +b=i a+b =a +b =i =-i b +a -i + = = =i a b ab - ' +å + 09 =-æ ' -å - +=0 +>0, -<0 - < ' -å' -å=-' ( - ) ( - ) -=0 -=0 -<0, -<0 a <b, c d a=-, b=, c=, d= a+b+c+d= 09 a=+'i a =-'i a+a =, aa = a- a- a - z = { }= = a+ a+ a + a- a - aa -(a+a )+ zz = = a+ a + aa +(a+a )+ -+ zz= =;7#; ;7#; z=a+bi (a, b ) z =a-bi (+i)z+iz =-+i (+i)(a+bi)+i(a-bi)=-+i a+bi+ai-b+ai+b=-+i (a+b)+(a+b)i=-+i a+b=-, a+b= a=, b=- z=-i -i z=a+bi z 0% z, z 0% 5% z 5% 096 z=a (+i)-a(-i)-(+i) z=(a -a-6)+(a +a-)i z=(a-)(a+)+(a-)(a+)i a=, z=-6 p= a=, z=0i q= p+q= z 0% p, q 0% p+q 0% 097 'a'b=-'ßab a<0, b<0 'ßd d 5 =-æ c<0, d>0 'c c 00

41 057 ~ 059 " a - b -" c +" (b+c) - a-d = a - b - c + b+c - a-d =-a-(-b)-(-c)-(b+c)-{-(a-d)} =-a+b+c-b-c+a-d =-d 098 z=(-i) -+i z=-i-+i z=-+(-)i -d a, b, c, d 0% 0% 0% z æ0 z, z 0 -=0 = z ()+()i 5% z æ0 z 5% 0% 099 b<a<0 a-b>0, b-a<0, -a>0, -b>0 'ƒa-b 'a ' -ßb + + 'ƒb-a ' -ßa 'b a-b a -b =-æ 5+æ 5 +{-æ } b-a -a b a-b =-æ 5+' -å-' -å -(a-b) =-' -å=-i 000 (+i)«n=, +i n=, (+i) =i n=, (+i) =(+i)(+i) =(+i) i=-+i n=, (+i) ={(+i) } =(i) =- n=8, (+i)«6 n=8 z 8(+i) =8_6=8 n=8, z=8 00 z=a+bi (a, b ) z =a-bi z+z =(a+bi)+(a-bi)=a+bi zz =(a+bi)(a-bi)=a +b z+z =+i zz a+bi =+i, (a +b )(+i)=a+bi a +b (a +b )+(a +b )i=a+bi a +b =a a +b =b, a=b a +(a) =a 0a =a, a(0a-)=0 a=0 a=; 0; a=0 b=0 z=0 a=; 0; z+z =a=_; 0;=;5#; 00 z=a+bi (a, b ) z =a-bi zz =a +b, z+z =a, z-z =bi 0 (z+)(z +)=zz +z+z + zz z+z (z-)(z +)=6zz +z-z - zz z-z z-z 0 (z-z ) 0 + = z+z, z z zz 00 a=a+bi, b=c+di (a, b, c, d ) a=b a+bi=c-di a=c, b=-d ab=(a+bi)(a-bi)=a +b =0 a=b=0 a=0 ( ) () a=i, b= a=bi a+0, b+0 () () a=i, b= a +b =i + =-+=0 a+0, b+0 () 0

42 RPM a +=a+ (a -)=a- (a+)(a-)=a- 0 =b(b+0) a=- 0 =0 a= (a -)=a+ (a+)(a-)=a+ a+ a+- a+,= = 5 (a+)(a-) a- a=-,0 =0 a=,0 = =+ æ, -=+ =-5 æ =-5 <, -(-)=+, =- =-, = =7 <-, -(+)-(-)=7 -+=7, -=6 =- - <, +-(-)=7 0 = æ, ++-=7 -=7, =8 =,, =- = - = - -= (-) -=-, = = -=-(-), -=-+ 0 =-, = =0 (-)(-)=0 = = 0 --=0 (+)(5-)=0 =-;!; =;5#; =0 - " - Ω - '5 = = ++=0 - " - Ω - 'ƒ- = = = 5 - ' i -8+8=0 -(-) " (-) - 8 = = 'ƒ- = 'i ++9=0-6 " = = =-;#; 009 D=(-) - (-)=>0 D =(-) -9 =0 ( ) D=(-5) - 5=-5<0 00 D=(-5) - =7>0 D=(-) - 5=-<0 D =(-) - =0 D =(-) - 9=0 D=(-) - =-7<0 D = - =5>0 D>0,, 0 -+k=0 D=(-) - k=9-k D>0 D=9-k>0 k<;(; D=0 D=9-k=0 k=;(; D<0 D=9-k<0 k>;(; k<;(; k=;(; k>;(; 0 +-=0 a+b=- ab=- a +b =(a+b) -ab=(-) - (-)=8 " - (-ç) a-b = =' =' ' 0 -+=0 a+b=, ab= 0

43 06 ~ 06 a b+ab =ab(a+b)= =6 a+b + = =;@; a b ab (a-)(b-)=ab-(a+b)+=-+= a b a(b+)+b(a+) + = a+ b+ (a+)(b+) ab+(a+b) = ab+(a+b)+ + = =;!); ;@; ;!); 0 +-=0 =- " - (-ç)=- '5 +-={-(-+'5 )}{-(--'5 )} =(+-'5 )(++'5 ) +5=0 =-5 = 'ƒ-5= 5i +5=(-5i)(+5i) -+=0 -(-) " (- ) - 'ƒ-7 '7i = = = +'7i -'7i -+={- }{- } 05 -(-+)+(-) =0 --=0 -{(+')+(-')}+(+')(-')=0-6+=0 --=0-6+=0 06 a, b +' -' (+')+(-')=-a, (+')(-')=b a=-, b= 07 a, b +i -i (+i)+(-i)=-a, (+i)(-i)=b a=-6, b= ab=k+5>0 k>-5,, -5<k - -5<k k+=0a, b ab=-k+<0 k> k> 00 a +=a(+) (a -a)=a-, a(a-)=a- a= 0 =0 a=0 0 =- a+ a+0 = a 0 (m+)(m-)=+m- (m +m-6)=m-, (m+)(m-)=m- m= 0 a -(+)a+-=0 a -a-a+-=0, (a-)=a -a- (a-)=(a-)(a+) a= (+5)a=+a +6 a= +0=++6 =0 0 (a-)-b+=+ (a-)=b- a+, b= (a-)=0 =0, () a=, b+ 0 =b- ( ) =0 0% a 0% 0% a=, b= 0 =0( ) b- a+, b+ = a- (), 08 -+k+5=0a, b D =(-) -(k+5)æ0 k - a+b=> =0 <, -(-)-(-5)=0 -= =-;$; 0

44 RPM <;%;, --(-5)=0 =-6 <;%; =-6 æ;%;, -+-5=0 =6 =: :,, =-;$; =: : -;$;+: := 05 + = - += (-) +=(-), = +=-(-), =0, = = " (-ç)ω = = <, -(-)-(-)= = < = <, --(-)= 0 =0 < æ, -+-= =,,, 07 - =+a æ;!;, -=+a =a+ -a <;!;, -(-)=+a =, -a =a+ = -a a++ =0 (a+)+-a=0 a=6 a= 00 -'+=0 -(-') ø(π-π') π-π μ = ' '6i = = 6 0 ( )-( )= ---(--)= --=0, (-)(+)=0 = =- 0 +m+m+=0- (-) +m (-)+m+=0 m=- m=- --5=0, (+)(-5)=0 =- =;%; ;%; ' '6i 6 0 -a+=0+' (+' ) -a(+' )+=0 +'+-a(+' )+=0 a(+')=6+' 6+' (6+')(-') a= 5= +' (+')(-') -' = =' ' - 0 = k +a+(k+)b=0 k+a+(k+)b=0 (+b)k+a+b=0 k +b=0, a+b=0 a=, b=- a-b= 08 (-) = -+ -+= -+ --=0 =-(-) " (-) - (-)= ' =0 (-)(-5)=0 = =;%; 05 ++=0a a +a+=0 a+0 a a++ =0 a+ =- a a a + ={a+ } - a a =(-) -=7 7 0

45 06 ~ ' (+')(-') +(+')+(+')(-+')=0 - +(+')-'=0, -(+')+'=0 (-)(-')=0 = =' 07 +' (+' )(-') -(+')+(+' )(-+' )=0 -(+')++'=0 (-){-(+' )}=0 = =+' 08 '+ ('+)('-) -('+)(-')+'('+)=0 -(+')+'('+)=0 (-'){-('+)}=0 =' ='+ a=', b='+ ( a<b) a-b='-('+)='- 09 Ω+Ω+=0 (' --)+('--)+=0 ' -(-')-=0 ' (') -'(-')-'=0 -('-)-'=0 =('-) "( ' -) +6' =('-) " -6 ' +6' =('-) ' ='-+'='- ='--'=-' = æ;!;, +-= +-=0, (+)(-)=0 =- = æ;!; = <;!;, -(-)= --=0 = ' <;!; =-' '- -'-, =-' = -' 0 = - ++ = - + = - æ-;@;, += - --=0, (-)(+)=0 =- = æ-;@; = <-;@;, -(+)= - +=0, (+)=0 =0 =- <-;@; =-, = = =0 æ0, --=0 = ' æ0 =+' <0, +-=0 =- ' <0 =--', =+' =--' (+')(--')=--' - -=" (-ç) " (-) = - - -= - <0, +-=-(-) +-=0, (+)(-)=0 =- = <0 =- 0 <, --=-(-) -=0 = ' 0 < æ, --=- --=0 = ' æ =+',, =- =+' -+(+')=-+' --' -+' 0 +(a+)+a =- =- (-) +(a+)(-)+a = a -a = a -a= 05

46 RPM a -a=, a -a-=0 a= ' a -a=-, a -a+=0 a= a (+') (-') =- 0 [] +[]-=0 ([]+)([]-)=0 []=-;#; []= [] []= < 05 [] -[]-=0 ([]+)([]-)=0 []=- []= [] []= < -[]-=0 <<, []= --=0, (-)(+)=0 =- = << <, []= --=0 = ' < =+', =+' 06 -[]= 0<<, []=0 = = ' 0<< <, []= -= = ' < =' <, []= - =- a 0% a 0% a 0% < =+' -= = < =,, =' = a=', b= a -b =(') - = [+] -6[]+=0 ([]+) -6[]+=0 [] +[] +-6[] +=0, [] -[] +=0 ([]-)([]-)=0 []= []= < < < < m (-)(6-)= =0 -+57=0 (-)(-9)=0 = =9 6- ->0 0<<6 = 09 cm cm, (+) cm ;!;{+(+)}=0, +-0=0 (-5)(+6)=0 =5 =-6 >0 =5 5cm 050 cm cm (-)(-) cm 9 cm (-)(-)=9-6-0=0, (-0)(+)=0 =0 =- > = =0(cm), 0 cm 0 cm, 0 cm 05 a % a{+ } 00 % a{+ }{- } a 9% 9 a{+ }{- }=a{- } = =900 =0 ( >0) 06

47 06 ~ k=0 D D =(-) -(-k)æ0 +kæ0 kæ-;!;, -+-k=0 D D =(-) -(-k)<0 -+k<0 k<, -;!; k< -;!; k< 05-5+k+=0 D D=(-5) -(k+)>0, 7-k>0 k<: : k 05 -(a-)+a-=0 D D =(a-) -(a-)=0 a -6a+5=0, (a-5)(a-)=0 a=5 a= -(a-)+=0 D D =(a-) - =0 a -a-5=0, (a-5)(a+)=0 a=5 a=-, a (k+) +k+k+=0 k++0 k+- D D a 0% a 0% a 0% =k -(k+)(k+)æ0-5k-6æ0 k -;5^;, k<- -<k -;5^; (k-a)+(k -6k+b)=0 D D =(k-a) -(k -6k+b)=0 k -ak+a -k +6k-b=0 (6-a)k+a -b=0 k 6-a=0, a -b=0 a=, b=9 a+b= 057 +(k-a)+k +a +b-=0 D D =(k-a) -(k +a +b-)=0 k -ak+a -k -a -b+=0 -ak-b+=0 k -a=0, -b+=0 a=0, b= a-b= m -(m-a+b)+m-a+=0 D D =(m-a+b) -m(m-a+)=0 m +a +b -am-ab+bm-m +am-m=0 (-a+b-)m+(a-b) =0 m -a+b-=0, (a-b) =0 a=, b= a +b =+= 059 +(am+b)+m +c+=0 D D=(am+b) -(m +c+)=0 a m +abm+b -m -c-8=0 (a -)m +abm+b -c-8=0 m a -=0, ab=0, b -c-8=0 a =, b=0, c=- a +b +c =+0+= (a+b)+ab+ -(b+c)+bc+ -(c+a)+ca -(a+b+c)+(ab+bc+ca) -(a+b+c)+(ab+bc+ca)=0 D, D =(a+b+c) -(ab+bc+ca)=0 07

48 RPM a +b +c -ab-bc-ca=0 ;!;{(a-b) +(b-c) +(c-a) }=0 a, b, c a-b=0, b-c=0, c-a=0 a=b=c a, b, c 06 +(a-)+-a +(a-)+-a=0 D, D =(a-) -(-a)=0 a -a-=0, (a-)(a+)=0 a=- a= - 06 (a-c) +b+a+c=0 a-c+0 a+c D D =b -(a-c)(a+c)<0 b -a +c <0 b +c <a ABCA> k +(-)-6 +7-k=0 -(-) ' D = D=(-) -(-6 +7-k) =5-0+k+ D, D, D=0 D' D' =5-5(k+)=0 5-00k-5=0 k= 06 -+=0ab a+b=, ab= b a a +b (a+b) -ab(a+b) + = = a b ab ab - = = =0a, b a+b=-, ab=;#; a +b (a+b) -ab = (a-b) (a+b) -ab - = =-;!; -;!; =0a, b a+b=, ab=;!; (-) - ;#; = (-) - ;#; (a-b) =(a+b) -ab= - ;!;= a-b =' a +b =(a+b) -ab= - ;!;=;&; +b++a + = +a +b (+a)(+b) (a+b)+ = +(a+b)+ab + = =;!^; ++;!; =0a, b a+b=, ab= ('a+'b) =a+b+'a'b =a+b+'aßb ( a>0, b>0) =+=6 'a+'b='6 ' a+b=0a, b a+b=-a, ab=b, +b+a=0a+, b+ (a+)+(b+)=-b, (a+)(b+)=a, (a+b)+=-b, ab+(a+b)+=a -a+=-b, b-a+=a, a-b=, a-b= a=-, b=- ab= 08

49 067 ~ (k+)+k-=0a, b a+b=k+, ab=k- (a-b) =(a+b) -ab=5 (k+) -(k-)=5 k -k=0, k(k-)=0 k=0 k= 0 (a -a+)(b -b+) =(a+-a+)(b+-b+) =(-a+5)(-b+5) =ab-5(a+b)+5 = = ;%; =0a, b a -5a+=0, b -5b+=0 a -a+=a, b -b+=b, a+b=5, ab= b a + a -a+ b -b+ b a = + a b a +b = ab (a+b) -ab = ab 5 - = =: : : : 5% 5% 50% =0a, b a+b=, ab=6, a a -a+6=0 a =a-6 a b+a + = a b ab b+a-6 + = ab (a+b)-6 + = ab -6 + = =;%; 6 --=0a, b a -a-=0 a =a+ b -b-=0 b =b+ a+b=, ab= a -a=0 a, a+ a+(a+)=- a(a+)=a -a a=- a=- a=- a -a=0, a(a-)=0 a=0 a= a 07 +(k+)+=0 a, a a+a=-(k+) k=-a- a a= a = a=- a= k= k=- k k= 07 a, a a+a=k+ k=5a- a a=k 6a =5a-, 6a -5a+=0 (a-)(a-)=0 a=;!; a=;!; k=;#; k=;@; ;#; ;@; 075 -a+a+=0 n, n+(n) n+(n+)=a n(n+)=a+ n+=a n +n=(n+)+, n -n-=0 (n-)(n+)=0 n= ( n) n= a=5 09

50 RPM =0a, b a+b=-;#;, ab=;!;, a+, b+ b a a+ +b+ =(a+b)+{ + } b a a b a+b a+ +b+ =(a+b)+ ab -;#; a+ +b+ =-;#;+ =-;(; ;!; {a+ }{b+ }=ab+ + b a ab =;!;++=;(; a+, b+ b a +;(;+;(;=0, +9+9=0 a=9, b=9 a+b= '- '+ + ='6 ' ' '- ' '+ _ = ' '- '+, ' ' -'6+=0 (-'i)+(+'i)=6 (-'i)(+'i)= -'i, +'i -6+=0 -'6+=0-6+= =0a, b a+b=, ab=-, a, b a +b =(a+b) -ab= - (-)=6 a b =(ab) =(-) = a, b -6+=0 a=-6, b= a=-6, b= 0% a, b 50% 0% a, b 0% 079 +a+b=0 +a+b=0 a+b=-, +(a+)+b-=0 +a++b-=0 a+b=-, a=-, b= -, (+)(-)=0, +-=0 p=, q=- pq= a, b -a-b=0 -i +i (-i)+(+i)=a, (-i)(+i)=-b a=, b=-5 a+b=- 08 p, q +p+q=0 +'5 -'5 (+'5)+(-'5)=-p (+'5)(-'5)=q p=-6, q= p-q=-8 a, b +a+b=0 -'5 = =-+'5 +'5 (+'5)(-'5) --'5 (-+'5)+(--'5)=-a (-+'5)(--'5)=b a=, b=- ab= m, n +m+n=0 --i -+i 050

51 069 ~ 070 (--i)+(-+i)=-m m= (--i)(-+i)=n n= ;!;, {-;!;}(-)=0, -5+=0-5+=0 08 a, b +a+b=0 +i +i = = =;!;+;!;i -i (-i)(+i) ;!;-;!;i {;!;+;!;i}+{;!;-;!;i}=-a a=- {;!;+;!;i}{;!;-;!;i}=b b=;!; f()= -+;!; f() - f()= -+;!;=;%; =0 =- " - 6=- 'i ++6={-(-+'i)}{-(--'i)} =(+-'i)(++'i) =0 =-(-) " (- ) - = i -+={-(+i)}{-(-i)} =(--i)(-+i) 5 ++ =0, =0 - " i = = i --i ++ ={- }{- } = (+-i)(++i) ;%; 0% a, b 0% f() - 0% =0 =-(-) "( -) - 5= i -+5={-(+i)}{-(-i)} =(--i)(-+i) a=-, b=-, c= a=, b=-, c=- abc= 087 ;!; ++=0, ++=0 =- " - =- i ;!; ++=;!;{-(-+i)}{-(--i)} ;!; ++=;!;(+-i)(++i) 088 f()=0a, b a+b=5 f(a)=0, f(b)=0 f(+)=0 +=a +=b a- b- = = f(+)=0 a- b- a+b = = = 089 f()=0 = f()=0 f(-)=f(0)=0 f( -)=f(0)=0 f( +)=f()=0 f(+)=f()=0 f( )=f()=0 090 f()=0a, b ab=6 f(a)=0, f(b)=0 f()=0 =a =b a b = = f()=0 a b ab 6 = = = f()=0a, b f(a)=0, f(b)=0 f(+5)=0 +5=a +5=b a-5 = = b-5 05

52 RPM f(+5)=0 a-5 b-5 ab-5(a+b)+5 = = = a+b<0, ab<0 a+b=(m-)<0 m< ab=-m<0 m>0, 0<m< 09 a, b D D =(k-) -(k +)æ0 097 a, b a+b>0, ab<0 a+b=a+>0 a>-;!; -8k+æ0 k ;&; ab=a-5<0 a<5 a+b=-(k-)>0 k< ab=k +>0 k,, k ;&; k 09, a, b ab=-k<0 k>, -;!;<a<5 a 098 a, b a+b=0, ab<0 a+b=-(a +a-)=0 a +a-=0, (a-)(a+)=0 a= a=- ab=a-<0 a<;!; 09 a, b D D ={(k+)} -(k +)æ0 8kæ0 kæ0 (k+) a+b=- <0 k + k +>0 -(k+)<0 k>- ab= k +>0 ab>0 k + k,, kæ0 095 a +b+c=0 D D=b -ac>0 ()=-;ab;<0 ()=;ac;>0 096 a, b, a=- 099 (a -)-=a(+) (a -a-)=a+ (a-)(a+)=a+ a=-,0 = =0 - " - - '7i = = 8 8 a=-, b=7 a+b= =+ <0, --(-)=+, = =;!; <0 =;!; 0 <, -(-)=+ = æ, +-=+ =,, = = =0 " - i = = 05

53 070 ~ 07 +i -i -+={- }{- } --i -+i -+= -+=;!;(--i)(-+i) a=;!;, b=+i, c=-i a=;!;, b=-i, c=+i a+b+c=;%; 050 a, b +a+b=0 -' +' (-' )+(+' )=-a (-' )(+' )=b a=-, b= ab= (a+)+a=0a, a a+a=a+ a=a+ a a=a a =a a=a + a -a+=0, (a-)(a-)=0 a=;!; a= a=;!;,a=;!; a=, a= a a= =0a, b a+b=-;#;, ab=- b a b(b+)+a(a+) + = a+ b+ (a+)(b+) (b +b)+(a +a) = ab+(a+b)+ (a+b) -ab+(a+b) = ab+(a+b)+ {-;#;} - (-)-;#; = --;#;+ : ª: = =-;!0(; -;!0(; -;%; (k-)+=0a, a+ a+(a+)=k- a(a+)= a +a-=0, (a-)(a+)=0 a= a=- k=5 k=- k>0 k= ' -(-')-(+')=0 ' (') -'(-')-'(+')=0 -('-)-'-=0 =('-) "( '- ) - (- '-) ='- ' k=0 D D =(-) - (-k)<0 +6k<0 k<-;@;, +-k=0 D D = -(-k)æ0 +kæ0 kæ-, - k<-;@; k -, =0 - =t(tæ0) t -t-=0, (t-)(t+)=0 tæ0 t=, - = -= =- = -(-)=6 æ(-) -(-)-=0 -=0, (-)=0 =0 = æ = <, (-) +(-)-=0 -=0, (+)(-)=0 =- = < =- -(-)=6 05

54 RPM 050 f()=0a, b f(a)=0, f(b)=0 f(-)=0 -=a -=b a+ b+ = = f(-)=0 a+ b+ (a+b)+ab+ = +6+ = = 05 -+=0a, b a+b=, ab= a+, b+ a++b+=(a+b)+=+=6 (a+)(b+)=ab+(a+b)+=++=8 6, 8 -(6+8)+6 8=0 -+8=0 05 a, b a+b=0, ab<0 a+b=a -a-=0, (a-)(a+)=0 a= a=- ab=a-<0 a<, a= [] -[+]+=0 [] -([]+)+=0, [] -[]+=0 ([]-)([]-)=0 []= []= < < 05 m (-)(-0)(m ) -(-)(-0)(m ) ;!; -(-)(-0)=;!;, =0 (-8)(-0)=0 =8 =0 >0 =0(m) 055 (+008) -(+008)-=0 +008=X X -X-=0, (X+)(X-)=0 0 m X=- X= +008=X =X-008 =-009 =-005 (a+009)(b+009)= , -b+" b -ac -b-" b -ac + =-;ab;=-5 a a b=5a -b+" b -ac -b-" b -ac _ =;Ça;=-6 a a c=-a a +5a-a=0 +5-=0, (-)(+8)=0 = = a+a - = = a -a = a -a= a -a=, a -a-=0 (a-)(a+)=0 a= a=- a -a=-, a -a+=0 D=- =-7<0, a= a= m=0 D D =-m<0 m>;!; +m+m +m-=0 D D 5=m -(m +m-)<0 -m+<0 m>, m m>;!; 059 +(m+)-=0 - -a, a -a+a=-(m+) (-a) a=- a = a=- a= a=-m=, a=m=- m - 05

55 07 ~ k=0a, b a+b=-, ab=k a + b =7 a +b + ab =9 (a+b) -ab+ ab =9 (-) -k+ k =9 k -k=0 kæ0 0 k=0 k k<0 -k-k=0 k=-0, k= (a +a)--a=0- +(a +a)--a=0 a +a-=0, (a+)(a-)=0 a=- a= a=-, -=0 = a=, --=0 (+)(-)=0 =- = a=-=, a== =- 0% a 0% a=- 5% a= 5% 05 a, b +a+b=0 +i -i (+i)+(-i)=-a, (+i)(-i)=b a=-6, b= -6, -(-6)+ (-6)=0-7-78=0-7-78=0 0% a, b 0% 0% 05 +(k+b)+k -a+b-k=0 D D =(k+b) -(k -a+b-k)=0 (b+)k+a+b -b=0 k b+=0, a+b -b=0 a=-, b= =0 æ, -(-)-=0 --=0, (-)(+)=0 = =- æ = a=-, b=- 0% 0% a, b 0% <, -{-(-)}-=0 +-6=0, (+)(-)=0 =- = < =-, =- = =- = æ, 0% <, 0% 0% 055 (k+-a) +(k+a+b)+k=0 D D =(k+a+b) -(k+-a) k=0 (k +a +b +ak+ab+bk)-(k +k-ak)=0 (a+b-)k+a +ab+b =0 k 055

56 RPM a+b-=0 a +ab+b =0 (a+b) =0 b=-a b=-a a-a-=0 a=, b=- k +k+k=0 k(+) =0 =- a+b+a=+(-)+(-)= =0a, b a+b=-, ab=-, a +a= f()= +a+b f(a)=a +aa+b= f(b)=b +ab+b= - a -b +aa-ab=0 (a+b)(a-b)+a(a-b)=0 (a-b)(a+b+a)=0 a+b a+b+a=0 a=-(a+b)=-(-)= a= a +a+b= b=-(a +a)=-=- f()= +- f(a)-=f(b)-=0 f()-=0a, b f() f()-=(-a)(-b)= +- f()= +- (a +b +-a-b+ab)-(a +b +ab+)=0 -a -b -ab-a-b-=0 a +b ++a+b+ab=0 (a+b+) =0 a+b+=0, a+b=- a +b -ab=(a+b) -ab(a+b)-ab a +b -ab=(-) -ab (-)-ab a +b -ab= a +b+c=0 '6 p p{-(+'6)}{-(-'6)}=0 p( --5)=0, p -p-5p=0 b=-p, c=-5p -;!;, a{+;!;}(-)=0, a{ -;@;-;!;}=0 a -;@;a-;!;a=0 b=-;@;a, b=-p=-;@;a p=;!;a c=-5p=-;%;a a -;@;a-;%;a=0, -;@;-;%;=0 -;%; -;%; =0a, b a+b=-, ab=- ( a + b ) =a +b + ab =(a+b) -ab+ ab =(-) - (-)+ - = a + b =' ='6, a b = ab = a, b -'6+=0 050 PBQ PB =PQ CQ = DQ =DP =- QBC BQ =+ PQD PQ =(-) +(-) BQ =PQ + =(-) +(-) -+=0 = ' 0<< =-' A B P - D - Q C 058 {+(a+b) } -(-a-b)+=0 D D =(-a-b) -{+(a+b) }=0 056

57 075 ~ , -,, 05,,,,,,,, 05 a+b+c=0 =-;ba;-;bc; ab<0, bc<0 -;ba;>0, -;bc;>0,, a+b+c=0 c=0 =-;ba; ab>0 -;ba;<0,, a+b+c=0 a=0 b+c=0 =-;bc; 055 = - =- æ0, <0 056 = + =+ <0, æ0 æ0 057 =+ =+ <0, æ0 æ0 058 =- + =-+ æ0, æ0,, 059 = -6=(-) - (, -) = bc>0 -;bc;<0, 050 = -8+7=(-) -9 (, -9) = 05 = f() - =f( ) - 05 =- -+=-{+;!;} +;%; {-;!;, ;%;} =-;!; =f() =f( ) 05 =;!; -;$;+;&;=;!;(-) + (, ) = 057

58 RPM 05 =-;!; +-=-;!;(-) +;&; {, ;&;} = =a(-+) +b, a+b= =a(+) +b, 6a+b= a=, b=- =(+) -, = +6+7 = =-;!; =-;!;(-) +8,, a>0 =b - b <0 b>0 a a, >0 c>0 a<0 =b - b >0 b>0 a a, <0 c<0 056 (0, ) =a + (, ) =a+ a= = + = (-, 0), (, 0) =a(+)(-) (, -6) -6=a(+)(-) a= =(+)(-), = --6 = =a +b+c (0, ), (, ), (, 6) =c, =a+b+c, 6=a+b+c a=, b=-, c= = -+ = =- =a(+) +b (-, ), (, ) 0550 a<0, b<0, -a-b=-(a+b)>0 =a-a-b 055 =(a-)+b- 5 a-=tan 5 = a= b-= b= a+b=6 6 a c 055 a+b+c=0 =- - b b ( )>0()<0 a c - >0, - <0 b b c a, c+b+a=0 =- - b b c a ( )=- <0, ()=- >0 b b 055 f()=(+m)+m+ -<< f()>0 f(-)æ0, f()æ0 f(-)=--m+m+æ0 mæ f()=+m+m+æ0 mæ-, mæ 055 << f() f()>0, f()<0 f()<0, f()>0 f()=a-, f()=a- f()>0, f()<0 a->0 a> a-<0 a<;@; =a-a-b 058

59 077 ~ 080 f()<0, f()>0 a-<0 a< a->0 a>;@; ;@;<a< 0559 f()=-;!;+ =f() f(a)=, f()=b f(a)=-;!;a+= a=0, ;@;<a< a f()=-+=b b=- a=0, b=- f() f() f(), f()f()<0 (a-a-)(a-a-)<0 (a-)(a-)<0 ;@;<a< a m>-m (-)m-+<0 f(m)=(-)m-+ 0<m< f(m)<0 f(0) 0, f() 0 f(0)=-+ 0 æ;!; f()=(-)-+ 0 5, ;!; 5 ;!; f() f(-)<0, f()<0 f(-)=-9+m-m-<0 m< f()=-m-m-<0 m>0 0<m< m 0557 f()=a+b a>0 f(-)=, f()= f(-)=-a+b= f()=a+b=, a=;6!;, b=;$; a+b=;#; 0558 f()=+k =f() f(-)=n, f()=n f(-)=-6+k=n f()=9+k=n - n=-5 n=-5 n=-5 k= f()=-+k -, f()=- f()=-6+k=- k=5 f()=-+5 f() =, f()=-+5= 056 =- =- <0 æ0 æ0 æ0, =- <0, -=-, = = f() =f( ) =f() =f( ) 056 =f( ) =f() æ0 æ0 - - =f() =f( ) = ,

60 RPM <-, =-++= - <0, =--(+)=-- æ0, =-(+)=- = = - æ0, = - <0, = -- = + - (æ0), =[ + (<0) ( -+ (0 <) \ - (æ) = { \ + (- <0) 9 -- (<-) = - - = - = - æ0, <0 = - =- <0, æ0 æ0 - - = =» -» ;!; 8=6 = , <-, =-(+)-(-)=-- - <, =+-(-)=5 æ, =++-=+ =7 ;!; (5+7) = = =7 6 æ0, æ0, += æ0, <0, -= <0, æ0, -+= <0, <0, --= ;!; 8= (, ) p=, q=, (0, ) =a 0- + a=- a+p+q=-++= p, q 0% a 0% a+p+q 0% = += æ0, æ0, 0568 = - - æ, =--=- <, =-(-)-=-+ - =-, M= = m=- M+m= 0569 = <-, =-(-)-(+)=-- - <, =-(-)+(+)=

61 080 ~ 08 æ, =(-)+(+)= = - ++ æ, =(-)++=- <, =-(-)++=-+ 0 =, M=8 =, m= Mm=6 057 f()= æ, f()=++-+-=- <, f()=++--(-)=+ - <, f()=+-(-)-(-)=-+6 <-, f()=-(+)-(-)-(-) =-+ =f() = 5 a=, b=5 a+b= <-, []=- =-[]=+ - <0, []=- =-[]=+ 0 <, []=0 =-[]= <, []= =-[]=- fi =, []= =-[]=0 =-[] 0 < < <-, - <-, [ ]=- =- - <0, - <0, [ ]=- =- 0 <, 0 <, [ ]=0 =0 =[ ] - <-, - <-;!;, []=- =- - <0, -;!; <0, []=- =- 0 <, 0 <;!;, []=0 =0 <, ;!; <, []= = fi =, =, []= = =[] - <-, []=- =-6 - <0, []=- =- 0 <, []=0 =0 <, []= = fi <, []= =6 =[]

62 RPM n, [-n]=[]-n =[-]=([]-) 0 <, []=0 =- <, []= =- <, []= =0 =, []= = =[-] <-, []=- =-- - <0, []=- =-- 0 <, []=0 =- <, []= =- =[] =- +k-k+7 =-(-k) +k -k+7 (k, k -k+7) = k -k+7=k k -6k+7=0 k = -m+m+5 m (-)m+- -5=0 m -=0, - -5=0 =, =9 P(, 9) P(, 9) =(-) +9= -+ -m+m+5= -+ m= 0577 = -a+a +a- =(-a) +a- - - (a, a-), a>0, a-<0 a<;#; a 0<a<;#; 0578 = -+a=(-) +a- (, a-) b = -b+={- } b b b {, - +} 8 b b = b=8, a-=- + a=- 8 0<a<;#; a+b=7 7 a 0579 = +a+b={+ } a - +b, - a ={-+ } a - +b- (, ) =(-) +, a a -+ =-, - +b-= a=-, b= a+b= 0580 = -8+7=(-) - (, -) = +-=(+) -5 (-, -5) (, -) a, b (-, -5) +a=-, -+b=-5 a=-, b=- a+b=-7-7 = % = +- 0% a, b 0% a+b 0% 06

63 08 ~ = + =(-) + -, =- +=-(-) + =(-) + -, = -+=(-) - =(-) + =(-) +, 058 = ++=(+) - =- +a-b=-(-a) +a -b (-, -) (a, a -b) a=, a -b= a=, b= ab= f()=a +b+c a>0 a, b b>0 ab>0 <0 c<0 ac<0, bc<0 f()=a+b+c ==0 a+b+c=0 f{;!;}=;!;a+;!;b+c =;!;<0 ;!;a+;!;b+c<0 a+b+c={;!;a+;!;b+c}<0 a+b+c={ a+ b+c}> f()=a +b+c a<0 a, b b>0 >0 c>0 f()=a+b+c =>0 a+b+c>0 = - =-;!;, >0 ;!;a-;!;b+c>0 a-b+c={;!;a-;!;b+c}> a>0 a, b b<0 <0 c<0 =c +b+a c<0, b, c, a>0 > a+b+c=0 =-;ba;-;bc;, -;ba;<0, -;bc;>0 058 f()=a +b+c a<0 a, b b<0 ab>0 >0 c>0 bc<0 f()=a+b+c ==0 a+b+c=0 f(-)=a-b+c =->0 a-b+c>0 f{;!;}=;!;a+;!;b+c =;!;, >0 ;!;a+;!;b+c>0 a>0, b>0, c<0 a<0, b<0, c>0 abc<0 a>0, b>0, c<0 =a +b+c a>0, a, b, c<0 < =- +=-(-) + (, ) - +=0 (-)=0 (0, 0), (, 0) 06

64 RPM = - + =- + a=-, b=0, c= a+b+c= ACB=;!; AB C 9=;!; AB AB =6 =- + - = A, B = A(-, 0), B(, 0), =f() (-, 0), (, 0) f()=a(+)(-) f(0)=- -8a=- a=;8#; 0589 (-, 0), (, 0) =a(+)(-) =a( --)=a(-) -a (, -a), += -a= a=;!; =;!;( --)=;!; --;#; a=;!;, b=-, c=-;#; f()=;8#;(+)(-) f(6)=;8#; 8 =6 6 A, B 0% 0% f(6) 0% a+b+c=-;#; 0590 = =a(-) +k(k ) (0, 7), (, ) a+k=7 a+k=, a=, k=- =(-) - = -8+7 a=, b=-8, c=7 abc= f()=m+m- f()>0, f()>0 f()=m+m->0 m> f()=m+m->0 m>;#;, m> 059 f()=m+m-6-0 f(-)<0, f(0)<0 f(-)=-6m+m-6<0 m>-;5^; f(0)=m-6<0 m<6 -;5^;<m<6 059 =a +b+c (-, ) a-b+c= (0, ) c= (, -) a+b+c=-,, m a+b+c=0 =-;ba;-;bc;, -;ba;<0 ;ba;>0 ab>0 -;bc;>0 ;bc;<0 bc<0, ac<0 06

65 08 ~ (-, -) 0597 = + - <-, =-(+)-=--7 æ-, =(+)-=+5 = + - =- - a=-, b=- a+b= = f() =f() æ0 <0 - =f() = f() - [ _(+)_]_= = <-;#;, =-(-)-(+)= a a>0, -;#; <, =-(-)+(+)=+5 æ, =-++= , c<0 a<0, ;&; ;&; 0599, f()=a(-)(-) ==- +=- (, -) f()=a(-)(-)=- a= f()=(-)(-) f()=(-)(-)= =a+b a>0 b>0 =a +b-ab a>0, a>0, b>0 -ab<0, c>0,, ac<0 060 = - =;!; æ, =- =;!; -=;!;, ;!;= = <, =-(-) =;!; -+=;!;, ;#;= =;@;, = =;@; ab=;$; 060 =f( ) =f() æ0, æ0,, 0605 =-+ (k, -k+) (k<0) =(-k) -k+ 065

66 RPM (-, ) =(--k) -k+, k +k-=0 (k+)(k-)=0 k=- k= k<0 k=- =(+) += ++7 a=, b=7 a+b= 0606 = , 0, <-, =-(+)--(-)=- - <0, =(+)--(-)=-+ 0 <, =(+)+-(-)=+ æ, 8 =(+)++(-)= ~ = ;!; = 060 f()= <0, f()= --=(-) - 0, f()= +-=(+) - - = + - M=f()= m=f(0)=- M+m= = +a-a a (-)a+ -=0 a -=0, -=0 =, = P(, ) = +a-a=(-) + = -+ a=- b 0608 =a +b+c=a{+ } - a a<0, b - <0 b<0 ab>0 ( ) a =- b - =- a=b ( ) a =->0 a-b+c>0 a+c>b ( ) b -ac a 0609 = + -, = + - = + - æ0 <0 06 =a+b a>0, =-, = 5 7 [ -a+b=- a=, b= a+b=6 a<0, =-, = 5 [ -a+b=6 a=-, b=a+b=-, b 7 +{- }= 06 =f() =f() æ0 æ0 =f() =f( ) =f( ) 06 =;!;(+) a, 066

67 085 ~ 087 =;!;(-a+) + =a- a-=5 a=6 (a-, ) b=a-=6-=5, c= a+b+c= 0% a, b, c 0% a+b+c 0% 06 (-, 0), (, 0) =p(+)(-) 6 =0, =6 6=-p p=- =-(+)(-)=-( +-) =-(+) +8 (-, 8) a=-, b=8 a-b=-9-9 0% 0% a, b 0% a-b 0% a 065 a + =9 =- + =- a,, 6 + æ0, æ a - 9 ā 9 5 _{ }=6, =6 a=;#; a a ;#; a + =9 60% a 0% 066 =+ =+ æ0 =+ æ0 - - =+k, =+k k =+k(-, 0) =+ =+k(-, 0) 0=-+k k= k k< k< =+ 0% =+k(-, 0) k 0% k 0% 067 =a +b+c a<0 b - >0 b>0 a c>0 f()=b +a+c f( )=b +a +c =b +a +c ( = ) =f() =f( ) 067

68 RPM 068 f()= , 8 <-, f()=-(+)+(-8)=- - <8, f()=++(-8)=- æ8, f()=+-(-8)= =f() = f() æ0 < = f() =k k 0<k k,,, 069 = +a =+a æ0, æ0,,, -6 = +a 6 -a -6 = +a ;!;(6-a)(6-a)=, (6-a) = 6-a= a= ( 0<a<6) -6 = +a =f{} a a = +a, =6-a = (6-a) =6-a =a a = f{} =k 6-a 6-a 0=- - +, - =;#; -= ;#; =;&; =;!; =k-k =k(-) =k-k k {;!;, 0} =k-k (, ), {;&;, 0} {;; ;;, ;#;} ;#;=;; ;; k-k k=;!; ;!; 06 f()= - + -a aæ, f()= - + -a =a-=5 a=6 6, 5 a<, f()= - + -a =-a=5 a=- -, 5, - 6, =f() k 06 = []- - <-, []=- = -- = - <0, []=- = -- = 0 <, []=0 = 0- = <, []= = - =0 fi =, []= = - = = []- - - = a a 5 =k-k - 7 =- - + =f{} =f{} = =

69 087 ~ =0 (-)=0 =0 = 0, =0 (-)(-)=0 = =, =0 D D =(-) - =8>0-8+= =0 D D = -(-) (-)=0 - +-= k=0 D D =(-) - k=-k D =-k>0 k< D =-k=0 k= D =-k<0 k> k< k= k> 068 +k+9=0 D D=k - 9=k -6 Dæ0 07 k -6æ0, (k+6)(k-6)æ0 k -6 kæ =-- ++=0 (+)(+)=0 =- =- k -6 kæ6 -, =-5 -+=0 (-) =0 =() 06 -+= -+=0 D D =(-) - =0 -+=0 -+=- -+=0 D D =(-) - =>0 -+=0 -+=-- +5=0 D D=0-5=-0<0 +5= =-7 -+5=0 D D =(-) - 5=-< = =0 D D=5 - (-6)=9> =+ -+=0 D D =(-) - = =+k -6+-k=0 D D =(-) - (-k)=8+k D =8+k>0 k>-8 D =8+k=0 k=-8 069

70 RPM D =8+k<0 k<-8 k>-8 k=-8 k<-8 a +a-=0, (a+)(a-)=0 a=- a= a -+= = +={+;!;} -;!; =-;!; -;!;, -;!; 067 =- +-7=-(-) -6 = -6, 068 =- ++=-{-;!;} +;; ;; -6 =;!; ;; ;;, ;; ;; =f(), - f(-)=0, f(0)=, f()=- - f(), -, f()= -+=(-) =f(), f(0)=, f()=, f()=6 f() 6, 6, 06 = -k+k -k+ -k+k -k+=0 D D =(-k) -(k -k+)>0 k->0 k> k 06 = +a+ak+k+b +a+ak+k+b=0 D D =a -(ak+k+b)=0 a -b-k(a+)=0 k a -b=0, a+=0 a=-, b= a+b= = -+k -+k=0 D D =(-) -kæ0 k = +(k-)+k + +(k-)+k +=0 D D =(k-) -(k +)<0 -k-<0 k>-;!; -;!;<k k 0,,,, 0,,,, = -+k 0% = +(k-)+k + 0% k 0% k 0% 06 = +(a-)+-a +(a-)+-a=0 D D=(a-) -(-a)=0 065 = +a+b -, -, +a+b=0 070

71 089 ~ 09 -;A;=-+, ;B;=(-)_ a=, b=- a+b= = --5 a, b a, b --5=0 a+b=, ab=-5 (a-b) =(a+b) -ab = - (-5)=6 a-b =6 --5=0 (+)(-5)=0 =- =5 5-(-)= a+b=0, a=5, b=6 = =0 (-5)(-)=0 =5 = = = 068 A, B a, b a, b -6+a=0 a+b=6, ab=a 8 a-b =8 (a-b) =6, (a+b) -ab=6 6-a=6 a=-7-7 = -6+a=(-) +a-9 (, a-9) = AB =8 A, B A(-, 0), B(7, 0) -6+a=0 -, 7 a=-7 A B 069 = - =-a -=-a, -+a=0 D D =(-) - a<0 a> 0650 = +a+a =+ +a+a =+, +(a-)+a -=0 D, D =(a-) -(a -)æ0 -a+æ0 a a 065 =+k = -+ +k= -+, -+-k=0 D D =(-) -(-k)>0 k>- =+k = -+5 +k= -+5, -+5-k=0 D D =(-) -(5-k)<0 k< -<k< k -, 0,,, = =+k =+k --k=0 D D=(-) - (-k)=0 9+8k=0 k=-;8(; -+;8(;=0, 6 -+9=0 (-) =0 =;#; =;#; = =;8(; {;#;, ;8(;} k=-;8(;, {;#;, ;8(;} 065 =- +a =-b - +a=-b +(-a)-b=0-, 5 07

72 RPM -+5=-+a, - 5=-b a=5, b=5 a+b= =a+b -a--b=0 +' -' (+' )+(-' )=a (+' )(-')=--b a=, b= a+b= 0655 = ++ =5+k ++=5+k, -+-k=0 - =- 8++-k=0 k= k= --6=0, (+)(-)=0 =- = B =5 +=8 B B(, 8) B(, 8) 0656 =+k = -6+ (a, a+k), (b, b+k) +k= -6+, -8+-k=0 a, b a+b=8, ab=-k 6'5 " (a- b) +( a+ k- b -k)ω =6'5 (a-b) =6, (a+b) -ab=6 8 -(-k)=6 k= =- ++5 = =-0, --5=0 (-5)(+)=0 =5 =- =5=0, =-=-6 (5, 0), (-, -6) "( - -5 ) + (- 6 )Ω =8'5 8' = -a+ =+ a, b -a+=+, -(a+)+=0 a+b=a+, ab= a-b =' (a-b) =, (a+b) -ab= (a+) - =, a +6a-7=0 (a+7)(a-)=0 a=-7 a= a>0 a= 0659 =+k = -5+5 A, B A, B +k= -5+5, -6+5-k=0 A = -+5-k=0 k=- k=- -6+8=0, (-)(-)=0 = = B A, B =- A(, -), B(, ) AB ="( - ) + ( +) Ω=' ' 0660 a= =+b = =+b, ++b-=0 D D = -(b-)=0 b= a+b=5 066 =-+ k =-(-k)+=-+k+ = - -=-+k+, --k-=0 D D =(-) -(-k-)=0 k+=0 k= = -+a P(, ) =-6+a a=5 07

73 09 ~ 09 =b+cp(, ) =b+c c=-b+ =b-b+ = -+5 b-b+= -+5, -(b+)+b+=0 D D={-(b+)} -(b+)=0 b -b+=0, (b-) =0 b= c=-b+= a+b+c=7 066 (-, ) m =m(+)+=m+m+ =- +5+ m+m+=- +5+, +(m-5)+m-=0 D D=(m-5) -(m-)=0 m -8m+=0 a, b a, b ab= =k - =k+ - =k+ = - =k+ = - =k+ 0<k+< -<k< a=-, b= - b-a=-(-)= =k+ = -- =k+ = -- =k+ 0<k+< -<k< k 0,, 0++= =f() (, 0), (, 0) f()=a(-)(-) (a>0) f(+)=a(+-)(+-) =a(+) f(+)=0 =0 = =f() (-, 0), (, 0) f()=a(+)(-) (a<0) f(+p)=a(+p+)(+p-) f(+p)=0 =-p- =-p+ -7 (-p-)+(-p+)=-7 -p+=-7 p= =f(+p) =f() -p f()=0 -, f(+p)=0 --p, -p -7 (--p)+(-p)=-7 p= 0668 =a +-a+ =-, b =a(+) +b =a +a+a+b =a +-a+, a=, a+b=-a+ a=, b=- ab= =a +b+c =-, =a(+) + (, 0) 0=a+ a=- =-(+) +=- -+ =a +b+c c= =- -a+5 =- b =-(+) +b = b =- -a+5, -8=-a, -8+b=5 a=8, b= a+b= 07

74 RPM 0670 f()=- +k-k =-(-k) +k -k =k, k -k, k -k=8, k -k-8=0 k f()=- -a+a- =-(+a) +a +a- =-a, a +a- g(a)=a +a-={a+;!;} -;%; g(a) a=-;!;, -;%; 067 =-;!; -+k =-;!;(+) ++k -;%; f() 50% g(a) 50% - =- +k, +k= k= =-;!;(+) + =-=, ==-5-5 (a-)(a-)=0 a= a= a= = a= 0675 =- +k=-(-k) +k kæ, k k =6 k= ( kæ) k<, k -+k=6 k=5 k<, k= =(-) +(+) -, (-) æ0, (+) æ æ =-(+) -(-) +5, (+) æ0, (-) æ =-, = 5 a=-, b=, c=5 a+b+c=6 6 k -+k k -+k k k 067 = <0, = --=(-) -5 0, = +-=(+) -5 - = + - M=0, m=- Mm= = -+5=(-) + 0 a 5, =0 =a a -a+5=, a -a+= =0 = = +(--) = ++8 =(+) +6 =- 6, = = = =- + + = +(-) = =5{-;5@;} +;5!; =;5@; ;5!; ;5!; 07

75 09 ~ = =- æ0, æ0 æ0, =-æ = +(-) = -+ ={-;!;} +;@; 0 =, =;!; ;@; =t t= +-=(+) - - t - t =t +(t+)-=t +t+ =(t+) - t=- m=-, t= M=, ;@; M+m= =t - t - t =t -t+=(t-) + t=-, 068 =-( --) +6( -+)- =-( --) +6( --)- --=t t= --=(-) - t tæ- =-t +6t-=-(t-) +6 t=, =t t= -+=(-) + t tæ =-t +(t-)+=-t +t-5 =-(t-) - t= +- =t +t+ - - t t t t t=, -5 -+= -+=0 (-) =0 = a=, b=-5 a+b= =-t +6t+8 =-(t-) +50 t= 50 m a= 0 -t +6t+8=0 (t-9)(t+)=0 t=9 t=- t>0 9 b=9 a+b= 0686 m (0-)m m =(0-)=- +0 =-(-0) +00 0<<0 =0, 00 m 00 m , =(0+)( ) = =-000(-0) = =- +a+b = =-(-) + =- ++ =- +a+b a=, b= a+b= 0689 f()= -+a={-;!;} -;!;+a - =;!;, - -5 t 075

76 RPM -;!;+a=;#; a= f()= -+ f(-)=, f()= 0690 =- ++-k - ++-k=0, --+k=0 D D =(-) -(-+k)>0 k<6 k = =-k =-k, -+k=0 D D =(-) - k=0 k=;!; -+;!;=0 9-6+=0 069 = +a+b +a+b=0 D D =a -b=0 b=a = +a+b = +a+b=, +(a-)+b=0 D D =(a-) -b<0 (a-) -a <0, -a+<0 a> 0695 = -a+ =-b -, -a+=-b, -(a+)++b=0 -, a+ +b -+=, -_= a=, b=-9 a+b=-8 (-) =0 =;!; =;!; = =;!; {;!;, ;!;} 0696 f()-g()=0 f()=g() =f(), =g() =- =5 069 = +a+b -, +a+b=0 -, a b -+=-, -_= a=-9, b=- a+b=- 069 = -+k- -+k-=0 D D =(-) -(k-)æ0 k = -(k+)+k -(k+)+k =0 D D =(k+) -k <0 k+<0 k<-;!;, k<-;!; k f()=a -a+b =a(-) -a+b a>0 = 0 =, -a+b=- =0, b=7, a=, b=7 a+b= = +a+b =- -' +a+b=-, +(a-)+b+=0 -' a, b +' (-' )+(+' )=-(a-) (-' )(+' )=b+ a=-, b=- a+b=- 076

77 096 ~ = -a+am-m+b -a+am-m+b=0 D D =(-a) -(am-m+b)=0 a -b-m(a-)=0 m a -b=0, a-=0 a=, b= a+b= 0700 =f() (-, 0), (, 0) f()=a(+)(-) (a>0) f(+p)=a(+p+)(+p-) f(+p)=0 =-p- =-p+ (-p-)+(-p+)= p=- =f(+p) =f() -p f()=0 -, f(+p)=0 --p, -p (--p)+(-p)= p=- 070 P(, ) +-=0 = = +(-+) = =0{- } =, =(-) +(+) -, (-) æ0, (+) æ æ- =, = = -a+6a-5 =(-a) -a +6a-5 =a, f(a)=-a +6a-5 f(a)=-a +6a-5 =-(a-) + f(a) 070 (, ) m -=m(-), =m-m+ = =m-m+, +(+m)-6-m=0 D D=(+m) -(-6-m)=0 m +6m+8= k+k=0a, b a+b=k, ab=k ' a-b =' (a-b) =8, (a+b) -ab=8 k -k=8, k -k-=0 (k+)(k-)=0 k=- k= = -6+0=(-) + k 0 k> =k 0 (k-) +=0, (k-) =9 k-= k=6 ( k>), k= = -+ =+k (a, a+k), (b, b+k) -+=+k, -6+-k=0 a, b a+b=6, ab=-k "Ω0 "( a- b) +{ (a +k )-( b+ k)} ="Ω0 " 5( a- b) ="Ω0 (a-b) =8, (a+b) -ab=8 6-(-k)=8 k= P (a, -a ) PQRS l l=a+(-a ) =-a +a+8 =-(a-) +0 (, 0<a<) 077

78 RPM 0<a< a=,l = -a+ =(-a) -a + =a-5, -0 (a-5-a) -a +=-0 5-a +=-0, a =6 a=6 ( a>0) 070 -=t t= -=(-) - - t - t 5 =(t+) -(t-) +5 =-t +6t+ =-(t-) + t= M=, t=- m=-6 M+m=- -a@+ - a-5 a a+ 07 =a +b+c - 9 t =-t@+6t+ 5-6 t=@- t =0 50% m, n 0% m+n 0% =-, AB = A, B -, =a(+)(-) (-, ) =a(-+)(--) a=- =-(+)(-) =- -+ a=-, b=-, c= abc=6 6 AB =A, B 0% 0% a, b, c 0% abc 0% - 07 = -a+a +a- =m-n -a+a +a-=m-n, -(a+m)+a +a-+n=0 D D=(a+m) -(a +a-+n)=0 a +am+m -a -a+-n=0 (m-)a+m +-n=0 a m-=0, m +-n=0 m=, n=;; ;; m+n=;; ;; ;; ;; 07 =- +a+ =-(-a) +a + (a, a +) - a, =a 6 a +=6, a = a= - a a<-, =- 6 --a+=6 a=-;%;, a=-;%; -;%; - a,a 0% a<-,a 0% a 0% 078

79 098 ~ f()=a +a+a +a =a(+) +a +a (-, a +a) a<0, a +a=6, a +a-6=0 (a+)(a-)=0 a=- a= a<0 a=- -- a>0 =, f()=a +5a=6, a +5a-6=0 (a+6)(a-)=0 a=-6 a= a>0 a= --, a=- a= k=0 - =k = - =k = - 0<k 076 =a +b-5 = -- - a<0,a 0% a>0,a 0% a 0% -Â Â 0<k =-5+,,,, --=-5+ +-=0, +-=0 (-)(+)=0 = =- (, -), (-, ), =k -=a+b-5, =a-b-5, a+b=, a-b=9 a=, b=- ab= =[ ] -[ ]+6 ={[ ]-} + [ ]=, < <6, = <-, =- ++ =-(-) +5 -, = -+ =(+) -5, = M=, =- m=- M+m= k=0 - =+k = - =+k = - =+k =+k =- +, - +=+k, ++k-=0 D D= -(k-)=0 k=;%; =+k(-, 0), 0=-+k k=, k= k=;%;, ;%;

80 RPM =0 (-)( ++9)=0 - 'i = = =0 ( --)=0, (-)(+)=0 =0 = =- 07 f()= - ++ f()=8-6+6+=0 f() f()=(-)( --) (-)( --)=0 = = ' 07 f()= ++0 f(-)=-8-+0=0 f() f()=(+)( -+5) (+)( -+5)=0 =- = i 07-8=0 ( -8)=0, (-)( ++)=0 =0 = =- 'i 075 f()= f()=6-++=0 f() f()=(-) ( ++) (-) ( ++)=0 - 'i = = f()= f(-)=--+7-6=0 f()= =0 f() f()=(+)(-)( ++) (+)(-)( ++)=0 =- = =- 'i 077 =t t -5t+=0, (t-)(t-)=0 t= t= = = = = = =0 ( +) - =0, ( ++)( -+)=0 ++=0 -+=0 - 'i 'i = = 079 -=t t -5t-=0, (t-8)(t+)=0 t=8 t=- t=8, --8=0 (-)(+)=0 = =- t=-, -+=0 = 'i, = =- = 'i 070 a+b+c=- ab+bc+ca= abc= ,, -(-++) +{(-) + + (-)} =0 -(-) = =0 07 -' +' 080

81 0 -, -', +' -(-')+(-' )(+' )-(+' )=a -(-' )(+' )=b a=-6, b= a+b= i --i, -+i, --i +(-+i)+(--i)=-a (-+i)(--i)=-b a=, b=-6 ab= = -=0 (-)( ++)=0 ++=0 ++=0 ++= = = =- =, ++=0 + +=( )fl +( ) + + += ++=0 =, ++=0 + =( ) +( ) + = += ( -+z= { +-z= 9 ++z=- + +=5 - --=, =, =- =, =- z=- =, =-, z=- ( --z=- 076 { -+z= 9 5--z=- + _ 7-5= + 7-5=-, - += + 6+=9, =k(k) =-k+ =k, =-k+ k-k++z= z=k- =k, =-k+, z=k- (k) 078 -=- =+ + =0 +(+) =0, +-6=0 +-8=0, (+)(-)=0 =- = =- =-, = = =- = [ [ =- = =0 (-)(+)=0 = =- = +- =8 + - =8, =8 = = =, = ( ) =- +- =8 (-) +(-)- =8, - =8 =-8 = 'i = 'i, = 'i ( ), = =- =-'i ='i [ [ [ [ = =- ='i =-'i 070 +=, =-8, t -t-8=0 (t-)(t+)=0 t= t=- = =- [ [ =- = 077 ( ++z= { ++z= 9 +-z=5 07 +=0 = æ 08

82 RPM =,, 7, (, ) (, 7), (, ), (, ) =0 ( -+)+( ++)=0 (-) +(+) =0, -=0, +=0 =, = =0 (+)(+)=0 --=0 (-)(+)=0 =, =- =- =- -k+=0 +k+=0 k= f()= -+ f()= f() - -0 f()=(-)( +-)=(-)(+)(-), (-)(+)(-)=0 = =- = f()= f()= f() f()=(-)( -9) f()=(-)(+)(-), (-)(+)(-)=0 = =- = f()= f()=0, f(-)=0 f() f()=(-)(+)( -+), (-)(+)( -+)=0 = =- = 'i f()= f()=0, f(-)=0 f() f()=(-)(+)( +), (-)(+)( +)=0 = =- = i 075 f()= f()=0, f(-)=0 f() f()=(-)(+)( -5-) f()=(-)(+)(+)(-), (-)(+)(+)(-)=0 =- =-;!; = = =-, = (-)_= =0 ( +6 +9)- =0 ( +) -() =0 ( ++)( -+)=0 ++=0 -+=0 =- 'i = 'i 077 =t t -7t+6=0, (t-)(t-6)=0 t= t=6 t=, = = t=6, =6 = = = =t t -t+6=0, (t-)(t-9)=0 t= t=9 t=, = = t=9, =9 = = = - +6=0 ( -8 +6)- =0 ( -) -() =0 08

83 0 ~ 0 ( +-)( --)=0 +-=0 --=0 =- '5 = '5-7 +=0 ( + +)-9 =0 ( +) -() =0 ( ++)( -+)=0 ++=0 -+=0 - '5 '5 = = 078 +=t t -t-5=0, (t+)(t-5)=0 t=- t=5 t=-, +=- ++=0, (+)(+)=0 =- =- t=5, +=5 +-5=0, (+5)(-)=0 =-5 =, =- =- =-5 = -=t (t-)(t-)-=0 t -6t+5=0, (t-)(t-5)=0 t= t=5 t=, -= --=0 D =+=>0 - t=5, -=5 --5=0 D =+5=6>0-5, (-)_(-5)=5 (+)(-)(+)(+6)+=0 {(+)(+)}{(-)(+6)}+=0 ( ++)( +-)+=0 +=t (t+)(t-)+=0, t -9t-=0 (t-)(t+)=0 t= t=- t=, +-=0 - t=-, ++=0, (-)_=- 079 (-)(+)(+)= {(-)(+)}{(+)}= ( +-)( +)= +=t (t-)t=, t -t-=0 (t-)(t+)=0 t= t=- t=, +-=0 D=+=>0 - a=- t=-, ++=0 D=-=-<0 b=, a-b= ;[%;+ =0 { + }+5{+;[!;}-=0 [{+;[!;} -]+5{+;[!;}-=0 {+;[!;} +5{+;[!;}-6=0 +;[!;=t t +5t-6=0, (t+6)(t-)=0 t=-6 t= t=-6,+;[!;=-6, +6+=0 =- ' () t=,+;[!;=, -+=0 'i = (), (-+' )+(--' )= =0 { + }-{+ }+5=0 [{+;[!;} -]-{+ }+5=0 {+ } -{+ }+=0 + =t 08

84 RPM t -t+=0, (t-)(t-)=0 t= t= t=, + =, -+=0 D=-=-<0 t=, + =, -+=0 D=9-=5>0 a a+ = a k+6=0 7-8+k+6=0 k= = (-)( +-)= = a+b=0-, ++-a+b=0, -++a+b=0, a-b=, a+b=0 a=, b=- ab= a +7b-b=0, 8+a+b-b=0, 7+9a+b-b=0, a+b=-, a+b=- a=-, b=- - -+= (-)(-)(+)= = = = a -(a+)-0=0 6+-8a-a--0=0 a= = (-)(+5)( ++)=0 ++= f()= -(a-) +a- f()=0 f() -(a-) a - -a+ -a+ 0 f()=(-){ -(a-)+} f()=0 -(a-)+=0 = -(a-)+=0 a=9 -(a-)+=0 D D=(a-) -6=0 a -8a=0, a(a-8)=0 a=0 a=8, a 9+0+8= f()= - +(k+)-k f()=0 - k+ -k f() - - -k f()=(-)( -+k) - -k 0 f()=0 -+k=0 D D =-kæ0 k k 0758 f()= + +k+k f(-)= k -k f() k f()=(+)( +k) k -0 f()=0 +k=0 D D=0- k<0 k>0 k> f()= + +(a-)-a f()=0 a- -a f() a f()=(-)( ++a) a 0 08

85 0 ~ 0 ++a=0 = ++a=0, D D =-a<0 a> D =, ++a=0 =-a=0 a, a> a> 0760 a+b+c=5, ab+bc+ca=9, abc=5 a +b +c =(a+b+c) -(ab+bc+ca) a +b +c =5-9=7 076 a+b+c=-, ab+bc+ca=, abc=8 (a-)(b-)(c-) =abc-(ab+bc+ca)+(a+b+c)- =8-+(-)-=0 a, a, a (a+0) a+a+a=- a=- a a+a a+a a=a a=a = a a a=-b b=-6a =8 a+b= a+b+c=-, ab+bc+ca=-5, abc=- + + a b c b c +c a +a b = a b c (ab+bc+ca) -abc(a+b+c) = (abc) (-5) - (-) (-) = =9 (-) 076 +a +b-=0-, a, b a +b =8 -+a+b=-a a=-(a+b) 9 50% % a b c -a-b+ab=b b=-(a+b)+ab -ab= ab=-, a +b =(a+b) -ab=8 (a+b) = a+b= a+b=, a=-(a+b)=0 a>0 a+b=-, a=-(a+b)=, b=-(a+b)+ab=, ab=8 076 a+b+c=-, ab+bc+ca=-, abc=,, a b c -{ + + } +{ + + }- =0 a b c ab bc ca abc ab+bc+ca = = =- a b c abc a+b+c = = =- ab bc ca abc = = abc + --=0 a=, b=-, c=- abc= a+b+c=, ab+bc+ca=, abc= -a, -b, -c -(-a-b-c) +(ab+bc+ca)+abc=0 + ++= a+b+c=0, ab+bc+ca=, abc=- a+b+c=0 a+b=-c, b+c=-a, c+a=-b (a+b)+(b+c)+(c+a)=(a+b+c)=0 (a+b)(b+c)+(b+r)(c+a)+(c+a)(a+b) =(-c) (-a)+(-a) (-b)+(-b) (-c) =ca+ab+bc= (a+b)(b+c)(c+a)=(-c) (-a) (-b) (a+b)(b+c)(c+a)=-abc= +-= a+b+c=, ab+bc+ca=-, abc=-a +-=0 085

86 RPM +b +c+=0a+, b+, c+ (a+)+(b+)+(c+)=a+b+c+=-b +=-b b=-6 (a+)(b+)+(b+)(c+)+(c+)(a+) =ab+bc+ca+(a+b+c)+=c -+ +=c c=7 (a+)(b+)(c+) =abc+(ab+bc+ca)+(a+b+c)+=- -a-++=- a= a+b+c= 'i -'i a (+'i)+(-'i)+a=-a (+'i)(-'i)+(+'i)a+a(-'i)=b (+'i)(-'i)a= a=, a=-, b=5 ab= ' +' a (-' )(+')a=-5 a=-5 (+' )-5=-+' 0770 =+i -i -i a (+i)(-i)a= a= (+i)+(-i)+=-a a=- (+i)(-i)+(-i)+(+i)=b b=6 a+b= 077 -i +i -+(-i)+(+i)= -(-i)+(-i)(+i)-(+i)=8 -(-i)(+i)=-0 -, -i, +i =0 f()= f()=8-+6+0= = -=0, (-)( ++)=0 =, ++= = =--= = -=0, (-)( ++)=0 =, ++=0 (+)(+ )=++ + =0+= fi + ++= +++ fi + ++= +++= fi + =( )fl fl +( )fl fl =+ =- + =( ) + ( ) + =+ = - = = =0 - (-)( ++)=0, -=0 = =( )fl +( )fl +( )fl +( )fl fl +( )fl fl =( ++)+( +) =0-= =- +=0, (+)( -+)=0 =-, -+=0 fl +fi =( ) = =- +- =-( -+)= a=, b=0 a+b= =8 + -= + _ 0=0 = -= = +-z=6 z=- a=, b=, c=- a+b+c= 0777 ( ++z= { +-z=6 9 -+z=- ( ++z=0 { +z=8 9 -z= 086

87 0 ~ 07 + =0 =5 5-z= z= +5+=0 = a=, b=5, c= abc= =, =, z= ( a+b-c= { c+b-b=5 9 b-c+c= c=;%; b-;%;= b=: 9 :, a+: 9 :-;%;= a=: 7 : 0779 = +=7 - - z+ = 5 5-z= - a=: 7 :, b=: 9 :, c=;%; ++z=7 - -z=0 _- _ = = =, =-, z= =, =-, z= ( ;[!;+;]!;=» 0780 { ;]!;+;z!;=» 9 ;z!;+;[!;= {;[!;+;]!;+;z!;}=- ;[!;+;]!;+;z!;=- - ;z!;=- z=-;!; - ;[!;=- =-;!; - ;]!;=5 =;5!; z=;6 0; ;6 0; (++z)=8 ++z=9 - z= - = - = a=, b=, c= a +b +c = + + =9 9 ( += (++z)= ++z= - z=- z=- - = - = = a=, b=, c=- a+b+c= ( ++z= (++z)=8 ++z= - =- - = - z= - + z = =-+= ( k++z= (k+)+(k+)+(k+)z= (k+)(++z)= k=-, 0 (++z)= ( ++z= ( +=5 { +z=6 9 z+=7 { +z=- 9 z+=- { ++z= 9 ++z= { +k+z= 9 ++kz= { ++z= 9 7++z=k - += - +=k- 087

88 RPM, k- k=6 6 70% k 0% ( a++z= (a+)+(a+)+(a+)z=6 (a+)(++z)=6 a=-, 0 (++z)=6 a=- a=, b=, a+b=- - ( += (++z)=9+k 9+k ++z= +k - z= -+k - = 9-k - =, -+k = >0 k> 9-k = >0 k<9 <k<9 k, 5, 6, 7, [ { +a+z= 9 ++az= { +z=6 9 z+=k =+ + =5 +(+) =5, +-=0, +-=0 (+)(-)=0 = =- ==, =-=- a=, b= a=-, b=- a +b -ab= 0789 [ + =0 = () + =0, = = = =6, =- =-6 a=6, b= a=-6, b=- ab= += [ ++ =5 =-- +(--)+(--) =5 +-=0, (+)(-)=0 =- = =-=, ==- a=-, b= a=, b=- a +b = [ ++ =- =- +(-)+(-) =- -+=0, (-)(-)=0 = = ==-, ==- =- - =0 079 [ -+ = (+)(-)=0 = =- = - + =, = = ', = ' ( ) =- - (-)+ =, = =, = ( ), =' =-' = =- [ [ [ [ =' =-' =- = a+b M=', m=-' M-m=' -=0 -= -- =0 079 [ + =0 088

89 07 ~ 09 (+)(-)=0 =- = =- (-) + =0, =0 = '5, = '5 ( ) = () + =0, = =, = 6 ( ), a, b a= 6, b= ( ) ab= 079 [ +- =0 (-)(-)=0 = = = + - =0, 0=0 () = () + - =0, = =, = ( ), a=, b= ( ) a +b = [ += (-)(+)=0 = =- = + =, = =, = ( ) =- (-) +(-) =, =6 = '6, = '6 ( ), ( '6)_( '6)= [ -+ =0 +- =0-9+5 =6 -+ = - _ -7+ =0 (-)(-)=0 = = = - +() =, = =, = ( ) = () - + =, =;7#; 'å 'å =, = ( ) 7 7 'å 'å, + -, -,, [ + = - _ -- =0 (+)(-)=0 =- = =- (-) +(-) =, 0=() = () + =, = =, = ( ), a=, b= ( ) a +b = [ -=6 _- -- =0 (+)(-)=0 =- = =- - (-)=, = =, = ( ) = - =, 0= (), a=, b= ( ) a-b = 0799 [ += -= -9+ =- -+ =7 + _ 6 -+ =0 (-)(-)=0 -=0 -=0 -=0, =;@; - ;@;+{;@;} =7, =9 =, = ( ) -=0, = - +() =7, = =, = ( ), a+b -5, -,, = 0800 [ + +-=6 089

90 RPM - _ +=0 =- (-) + +(-)-=6 5 --=0, (-)(5+)=0 = =-;5#; =-, = =;5(;, =-;5#; a, b a=-, b= a+b=- 080 [ -++=9 _- 5-= =5- (5-) -(5-)+= -5+=0, (-)(-)=0 =;!; = =-;&;, =;!; =, = a, b a=, b= ab= 080 [ - -=- =- +(-) +(-)=, = = =- =, =0 =-, =- + (-)+(-)= [ -+= + += + ++= +-=9 +-=- - _ += =- +(-)-=- -7+=0, (-)(-)=0 = = =, =- =, =-5 (a+b) (-) = 080, t -(+)t+=0, t -8t+5=0 (t-)(t-5)=0 t= t=5 a<b a=, b=5 a -b =9-5= =u, =v v+u=7 v=7-u uv=880 u(7-u)=880, u -7u+880=0 (u-6)(u-55)=0 u=6 u=55 u=6v=55, u=55v=6 u=6, v=55, +=6, =55,, t -6t+55=0 (t-)(t-5)=0 t= t=5 = =5 [ [ =5 = u=55, v=6, +=55, =6,, t -55t+6=0 55 " ' 9 t= =,, + = (+) = + + =-= += +=, =-6,, t -t-6=0 (t-)(t+)=0 t= t=- +=-, =-6,, t +t-6=0 (t+)(t-)=0 t=- t=, = =- =- = [ [ [ [ =- = = =- + M=9, m=-9 M-m= =u, =v u+v=-5 [ u -v=7 090

91 09 ~ 0 + u +u-=0 (u-)(u+)=0 u= u=- u=v=-6, u=-v=- u=, v=-6, +=, =-6,, t -t-6=0 (t-)(t+)=0 t= t=- u=-, v=-, +=-, =-,, t +t-=0 (t+)(t-)=0 t=- t=, =- = =- = [ [ [ [ = =- = =- a-b [ + =8 =-+a +(-+a) =8, -a+a -8=0 D D =a -(a -8)=0, a =6 a=6 ( a>0) [ += =-+ +(-+) =a, -+-a=0 D D =(-) -(-a)=0, -8+a=0 a= 080, t t -(a-)t+a +=0 D, D =(a-) -(a +)æ0, -6a+5æ0 a ;6%; a ;6%; 08 [ +=a + =a +=a +-=0 =-+a +-(-+a)=0, +-a=0 D D = -(-a)<0, +a<0 a<- a ,, (>) + =7 [ 0++0+= (+)= += =- +(-) =7, -+=0 (-)(-8)=0 = =8 =, =8 =8, = ,, 8 (+)=8 += + =0 (+) -=00 -=00 =8, t -t+8=0 (t-6)(t-8)=0 t=6 t=8 =6 =8 [ [ =8 =6 8 08, r, r r p+r p=p r +r =6 pr +pr =0p r +r =0 r =6-r r +(6-r ) =0, r -6r +8=0 (r -)(r -)=0 r = r = r =, r = r =, r = r -r r -r = 0 09

92 RPM r, r 0% r, r 0% 0% a=-k- (-k-) +k(-k-)+k+=0 k+6=0 k=-;#; 085, m, m + =50 [ (-8)(+)=+8, 8<<50, 0<<50-8=80 =+0 (+0) + =50, +6-0=0 (+0)(-)=0 = =-0 >0 = =8, 8 m, m 8 m, m 086 a a +aa+=0 [ a +a+a=0 - (a-)a+-a=0 (a-)(a-)=0 a= a= a=, ++=0 a=, +a+=0 a=-, a+a=- 087 a a +(m+)a-=0 [ a +(m+)a-6=0 - -a+=0 a= a= +m+-=0 m= m=, = 088 a a +ka+k+=0 [ a -a-k -k=0 - (k+)a+k +k+=0 (k+)a+(k+)(k+)=0 (k+)(a+k+)=0 k=- a=-k- k= =0 (+)(-)=0 =- = f()= -(a-) -(a-)-a f(-)=0 f() - -a+ -a+ -a - - -a- a - -a+ -a 0 f()=(+){ -(a-)-a}=(+) (-a) f()=0 =- =a a=- a= a a, b (a<b) a+b=m+ ab=m+ - _ ab-(a+b)=-, (a-)(b-)= a, b a-=, b-= a=, b= +=m+ m= =0 (-)-(-)-0=0, (-)(-)=0, , = = [ [ = = =0 (-5)-5=0, (-5)-5(-5)-5=0 (-5)(-5)=5, (, ) (6, 0), (0, 0), (0, 6) 09

93 0 ~ +++=5 (+)+( +-)+=5 (+)+(+)(-)= (+)(+-)=,, =-5 =- =- = [ [ [ [ =5 = =5 = =(9 +6+ )+( -+) =(+) +(-) =0, +, - +=0, -=0 =-;@;, = +=;$; ;$; =0 D D =() -9( -+)æ0 085 f()= f(-)=0, f()=0 f() f()=(+)(-)( -+), (+)(-)( -+)=0 =- = = 'i 086 f()= f()=0, f(-)=0 f() f()=(-)(+)( ++), (-)(+)( ++)=0 ++= , (-) 0 -=0 = = 9 ++=0 (+) =0 =- += =0 -(-)+(5-8+5)=0 D D =(-) -(5-8+5)æ0 -+ 0, (-) 0 -=0 = -6+9=0, (-) =0 = +=5 5 -(-)+(5-8+5)=0 -(-)+(-) + -+=0 {-(-)} +(-) =0 =-, = =, = +=5 ( -+z=0 087 { +-z= 9 -+z=5 - _ -+=-5 + _ 5-= + =8 = = -+=-5 =-, =, =- ++z=5 z= a=, b=-, c= abc=- 088 a+b+c=, ab+bc+ca=-, abc=-5 (a+b)(b+c)(c+a) =(-c)(-a)(-b) =8-(a+b+c)+(ab+bc+ca)-abc =8- + (-)+5= 09

94 RPM 089 f()= +a+6 f(-)=(-) +a (-)+6=0 a=-7 f()= f() f()=(+)( -+) =(+)(-)(-), (+)(-)(-)=0 =- = = a=-7, a=, b= a+a-b= ( +z=8 { +z= z= _5- _ -+z= + z= z= z=, =, = ++z=6 08 -i +i a (+i)+(-i)+a=a+ (+i)(-i)+(+i)a+(-i)a=b (+i)(-i)a=a a=, a=, b= a+b=+i 08 +a +b=0+i =+i (+i) +a(+i) +b=0 (+i) =+i-=i (i) +a i+b=0, b-+ai=0 a, b b-=0, a=0 a=0, b= 08 a+b+c=, ab+bc+ca=, abc=;!; b+c c+a a+b + + a b c -a -b -c = + + a b c ={ + + }- a b c ab+bc+ca = - abc = -= ;!; 08 (+i)( +a-)=0 -i a, b a, b +a-=0 -i+a+b=-i-a=6-i a= f()= - +- f()=0, f(-)=0 f() f()=(-)(+)( -+) -+=0 a a -a+=0 a a-+ =0 a a+ = a =- (-) + + =0, () æ0, æ0 -=0, +=0 =, =- +=- 087 = -=0, (-)( ++)=0 =, ++=0 (+)(+ )(+ )(+ )(+fi )(+fl ) =(+)(+ )(+)(+)(+ )(+) =(- )(-)(- )(-) =fl =( ) = ;[!;-;]!;=;6!; =;6!; 6-6=, +6-6=0 (-6)(+6)=-6, -6æ-5, +6æ7 09

95 ~ , = = = =5 [ [ [ [ = =6 = =0 + 5 =- - + =, = =, = ( ) = + =, =; 6; = ;!;, = : : ( ) +=7 089 [ + =5 + =(+) - =7 -=5 = +=7, =, t -7t+=0 (t-)(t-)=0 t= t= =, = =, = =, = a-=, -=b a=;%;, b=- ( a, b) =, = a-=, -=b a=, b=, a+b= ( -+z=5 080 _+ +z=8 + 8+z=6 +z=8, z ;[!;=X, ;]!;=Y, ;z!;=z ( X+Y+Z= { X-Y+Z= 9 X+Y+Z= - _ Y=-, X+Z=0, X+Z= - 0 X+0 Z=- X, Y 08 [ { +-z= z= -- =8 + = - _8 --6 =0 (+)(-)=0 =- =, = =- [ [ [ [ (a-b) (a+) -a=0 (+)( +a-a)=0 =- -a-a=0 a=;!; +a-a=0 D, D=a +a=0, a(a+)=0 a=0 a=-, a ;!;+0-=-;&; =- = =0 ( -)+( +)=0 ( -+)+( ++)--=0 (-) +(+) =5, =0 =- = =- [ [ [ [ =- =- =- =- =0 = = = [ [ [ [ =0 =- =0 =- +, f()=0a, b, c f(-)=0a', b', c' a'-=a, b'-=b, c'-=c, a'=a+, b'=b+, c'=c+ =: : =;!; =-: : =-;!; a'+b'+c'=(a+)+(b+)+(c+) =(a+b+c)+ =+= 085 a, b (a<b) 095

96 RPM a+b=m ab=m+5 - ab-(a+b)=5 (a-)(b-)=6 a, b a-=-, b-=- a-=-, b-=- a=-, b=- a=-, b=- m=a+b= = 086 [ ++ = +=u, =v + =(+) -=u -v u -v+u= u -v= - u-v= v=u- u -u=0, u(u-)=0 u=0 u= u=0v=-, u=v=0 u=0, v=-,, t -=0 (t-)(t+)=0 t= u=, v=0,, t -t=0 t(t-)=0 t=0 t=, = =- =0 = [ [ [ [ =- = = =0 (, -), (-, ), (0, ), (, 0) ;!; -;!; =;#; 087 a a +(k-)a+k=0 a -(k+)a+k=0 - ka-k=0, k(a-)=0 k=0 a= - k=0, -=0 - a=, +(k-)+k=0, k=- k=-;!;, k-a= {-;!;}-=- - a 0% a 0% k 0% k-a 0% 088 f()= -5 +a+b f(-)=(-) -5 (-) +a (-)+b=0 -a+b-=0 f()= -5 +a +b=0 a+b-=0, a=0, b= f()= f() f()=(+)(-)( +-) f()=(+)(-)(-)(+), (+)(-)(-)(+)=0 a=, b=- ( a>b) a =-;#; b -;#; -, 0% a, b 0% a, b 0% 0% a b 096

97 ~ a-, a, a+ a-+a+a+=a (a-)a+a(a+)+(a-)(a+)=6 (a-)a(a+)=-b a =7 a= a=, a=9, b=- a=-, a=-9 a>0, a=9, b=- a+b=-5-5 a-, a, a+ 0% 0% a, b 0% a+b 0% a=b a= p, q p=b, q=a b=p, a=q, a= +a+b=0 p+q+=0 p+q=-, pq=-6 a +b =p +q =(p+q) -pq =+= ( -+z=- 085 { -+-z=a 9 -+bz=0 _ -+6z= z=a-8 =z-a+8 -(z-a+8)+z=- =z-a+, (z-a+)-(z-a+8)+bz=0 (b-5)z=a- b-5=0, a-=0 a=, b=5 a=, b= cm (-)(+)(+)=;%; + +-6=;%;, ;#; - -+6=0-8 -+=0, (-)( --6)=0 =(cm) 8cm 8cm cm 0% 0% 0% 085 a a +aa+b=0 [ a +ba+a=0 - (a-b)a+b-a=0 (a-b)(a-)=0 a=b a= 085 f(a)=f(b)=f(c)= f()-=0 a, b, c, f()-=(-a)(-b)(-c) f()=(-a)(-b)(-c)+ f()=0 abc-=5-= 085 a cm, b cm, c cm ( (a+b+c)=8 { (ab+bc+ca)=8 9 abc=8 ( a+b+c=7 { ab+bc+ca= 9 abc=8 a, b, c =0 (-)(-)(-)=0, cm, cm, cm A B 097

98 RPM B B 09 A A B A AB =" + =5(cm) AB =" 5 + ='å9(cm) AB =" 6 + ='å7(cm) A B 5cm 0857 () a=-, b=- a>b a <b , A,B,C a, b, c =, =0, =8 a+b b+c a+c a+b=; ;, b+c=; 0;, a+c=;8!; (a+b+c)=; 0; a+b+c=; 0 =: 7º:=6.8 a+b+c A, B, C A, B, C %, %, z% A, B, C 5 % ;0{0; +;0}0; +;0Z0; ++ _00=5 ++z=75 A B % ;0{0; +;0}0; + _00= +=0 B C 6 % ;0}0; +;0Z0; + _00=6 +z=80,, =0, =0, z=5 C 5 % 5 % =-, - =-6, =, = =-,, ;$;=, ;$;= - ;]{; (-)> +5-5> ->- < < ;#;- æ 6 9-(-)æ, 9-+æ 5æ-0 æ- 086 a-8æ-a+ (a-)æ-(a-) a<, a-<0 a (a-)>a a a->0, a>,> a- a a-<0, a<,< a- a-=0, a=,0 > 086 a+ a+ (a-) a- a->0, a-<0,æ a-=0,0 0 æ

99 5 ~ < -<-< << << æ æ5 - æ7 f()= +-6 =f() f()<0 -<< =f() << - æ;&; 0867 æ, (-)< < æ < =0 (+)(-)=0 =-;!; = =f{} <, -(-)<, -<- >;@; < ;@;<< f()= -- =f() f()æ0 -- -, ;@;<< -;!; æ -;!; æ 0868 < + <6 <+<6-6<+<- <+<6 0<<5 0<<;%; -6<+<- -7<<- -;&;<<- 087 f()= -+5 f()=(-) + =f() f()>0 =f() 5, -;&;<<- 0<<;%; =0 (+6)(-)=0 =-6 = f()= +- =f() f()<0-6<< =f() << 087 f()= -6+ f()=(-) + =f() f()< f()= +8+ f()=(+) =f() f() 0 =- =- =f() =f() =0 (+)(-)=0 =- = f()= --6 =f() f()>0 <- > >0 +-6<0 +-6=0 (+)(-)=0 =- = - -6 =f() <- > 0876 f()= -+ f()=(-) =f() f()> f()>0 =f() <- > f() 0 =f() - =f() 099

100 RPM <0 (+5)(-)<0 -;%;<<;#; >0 (-)(-)>0 <;@; > (+)(-) 0 -;!; æ0 (-)(+)æ0 - æ;!; 0890 æ0, --<0 (+)(-)<0 -<< æ0 0 < <0, +-<0 (-)(+)<0 -<< <0 -<<0, -<< -<< æ -æ - - -æ -æ0 (+)(-)æ0 - æ æ0, - æ =0 =- '7 +-æ0 --'7 æ-+' =(-) æ0 -+>0 +;!; =(+) æ0 ++<0 +;!; =(-) æ0 -+9æ ={-;!;}+;&;æ;&; -+> ={-;%;}+;8&;æ;8&; -5+< æ(-) -+æ0 -+=(-) +æ 089 (+)(-)<0 --<0 (+)(-)>0 --8>0 (+)(-) (-)(-)æ0 -+æ0 089 = +k+ +k+=0 D D=k -8<0 -'<k<' -'<k<' 089 =- +-k+ - +-k+=0 D D =-(-) (-k+)<0 k>6 k> =- +k-k - +k-k=0, -k+k=0 D D =k -k 0, k(k-) 0 0 k 0 k ={-;6%;}+;!!;æ;!!; >+ >- +-5<0 (+5)(-)<0-5<<, -<< -<< 00

101 9 ~ æ0 (+5)æ0-5 æ (+6)(-) 0-6, <0 (-)(-)<0 ;!;<< ++9æ0 (+) æ0, ;!;<< æ0, (-)(-)æ0 æ +<+ --8<0, (+)(-)<0 ;!;<< -<<, -< < -< < 0900 f()= -k+9 f()=0 D =(-k) - 9æ0 k -9æ0 (k+)(k-)æ0 k - kæ f()=-k+9>0 -k+0>0 k<5 =f() =k k>,, k k<5 090 f()= -k+-k f()=0 D =(-k) - (-k)æ0 k +k-æ0, (k+)(k-)æ0 k - kæ f()=-k+-k>0 k<5 -k+>0 k< =f() =k k<,, k k f()= -k++k f()=0 f()=-k++k<0 k<- 090 a>b a+c>b+c c>d b+c>b+d, a+c>b+c>b+d a+c>b+d ( ) a>b, c>0 ac>bc b>0, c>d bc>bd, ac>bc>bd ac>bd ( ) () a=, b=, c=, d= ;ca;=;#;<;db;=;@; (), k - k<-, 090 () a=, b=- ;a!;=;!;>;b!;=-;!; () a=, b=, c=- ac=-<bc=- () a=, b=- a =>b = () a=, b= ;a!;=;!;<;b!;= a>b, 0905 () a=-, b=-, c=- a>b>c ac=, bc=6 ac<bc () a>0>b b-a<0, ab<0 b-a ;a!;-;b!;= >0 ;a!;>;b!; () ab a >b a -b >0 (a-b)(a+b)>0 a<0, b<0 a+b<0 a-b<0 a<b ( ) a -b =(a-b)(a +ab+b ) a>b a-b>0, a +ab+b ={a+;b;}+;#;b æ0, a>b a +ab+b >0 a -b >0 a >b ( ), a - a - - -;!;, 0

102 RPM + - -;!; a+ 6 a+=6 a= <, <, 0<+ 5 -<-< -< 6 -<-< a=-5, b= a+b= = =- 0<+ 0<-+, 0<- < ;!;< ;@; - - -, M=5, m= M-m= ;!;< ;@; 090 a -aæ6- (a -6)æa- 0 æ() a -6=0, a->0, a=, a> a= a-b=0, a-b<0, b=a, -a<0 a>0, b>0 a+b>a-b (a+b)>a-b b=a a>-a >-;@;( a>0) <6 <-, 7 -(-)-(+)<6 >- 5 7 <- - <<- 5 - <, -(-)+(+)<6 < - < - < æ, (-)+(+)<6 < æ 7,, - << 5 -, æ- -æ0,, -æ- 0 æ -<0, >, -(-)æ- æ;#;, æ;#; - - <, -(-) - æ;!; 09 a +a<+ (a -)<(-a) 0 <( 0) a -=0, (-a) 0, a=, aæ a= 09 a->b+ (a-)>b+ a-=0, b+<0 a=, b<- b - a+b +(-)= a(-)>b(-) (a-b)>a-b < ;!; < æ, - - æ0 æ æ, æ;!; < - < <, <-(-)<, -<-<- -<< æ, <-< <<5, -<< <<5 0

103 0 ~ < - < -<-<- <-< -<< << <6-6<-<6 -<<0 -<<5 a=-, b=5 b-a=6 -a > -a<- -a> a a < - > + <b > a a -=b, += a=, b=- a+b= >6 <-, -(+)+(-)>6 <- - <, (+)+(-)>6 > - < << æ, +-(-)>6 >0 æ æ,, <- > <- > 098 (a+b)+(a-b)<0 (a+b)<-a+b >-;!; a+b<0 -a+b > a+b -a+b =-;!; a+b a-6b=a+b, a=7b a=;&;b ;&;b+b<0 b<0 (a-b)+b-a>0 ;!;b-: :b>0, ;!;b>: :b b<0 < 099 (a-)>a (a-) <9 a (a-) a-<0 < =a a- a =9 a= a-<0, a< a=- 090 (a-b)+a-b<0 (a-b)<b-a <- a-b>0 b-a < a-b b-a =- a-b b-a=-6a+b b=a a-a>0 a<0 (a-b)+a+b<0 -a+a<0, a>a a<0 < < 09 (a-b)+a-bæ0 (a-b)æb-a a-b=0, b-a>0 a=b b-b>0 b<0 a=b (a-b)+a+b>0 b+5b>0, b>-5b b<0 <-5 09 a +(b-m)+c-næ0 a +b+cæm+n <-5, =a +b+c =m+n f() 0 =f() - 09 f()g()æ0 f()æ0, g()æ0 f() 0, g() 0 f()æ0, g()æ0 a b f() 0, g() 0 c d, f()g()æ0 a b c d a b c d 095 0<g()<f() g()>0 g()<f() g()>0 -<<8 0

104 RPM g()<f() =f() =g() < >7, -<< 7<<8 a=-, b=, c=7, d=8 a+b+c+d= a, b --7=0, = ' a=-', b=+' a-b=-'-(+')=-' (-5) æ0 =5 099 a<0 a -a+a <0, (-a)(-a)<0 a<<a ( a<0) -(a-)+a -a 0 -(a-)+a(a-) 0 (-a)(-a+) 0 a- a 5 (a-)+(a-)+(a-)+(a-)+a=5 5a-0=5 a= a<<a >0 (-) > (+) 0 =-;!; 9 æ æ0, (-) æ0-9> -+9<0, (-) < (-)(+) a +b+c>0 ;7!;<<;!; a<0 ;7!;<<;!; {-;7!;}{-;!;}<0, -;ª;+; ;<0 a a -;ª;a+; ;a>0 b=-;ª;a, c=; ;a c +b+a>0 ; ;a + {-;ª;a}+a> æ0 --=0 = ' (-+')(--')æ0 -' æ+' -5+>0 (-)(-)>0 ;7@; -;7(;+<0 ( a<0) -9+7<0, (-7)(-)<0 <<;&;, 5 < >;#; 5-5+6={- } {- } + æ ={+;!;} +;!;æ0 {+;!;} +;!;æ;!; -9 +-<0 9 -+>0 (-) >0 (-) æ0 +;@; æ (-5) a+b<0 -<< (+)(-)<0, --<0 a=-, b=- -b-a<0 ++<0, (+) <0 09 a +b+a+<0 -'<<+' a>0 -'<<+' (-+')(--')<0, -6+6<0 a>0 a a -6a+6a<0 a +b+a+<0-6a=b, 6a=a+ 0

105 ~ a=;!;, b=- a +b+c<0 <- > a<0 <- > (+)(-)>0, --6>0 a<0 a a -a-6a<0 a +b+c<0 -a=b, -6a=c b +a-c<0 -a +a+6a<0, -a( --6)<0 a<0 --6<0 (+)(-)<0 -<< -;@; -<< a +b+a+=0 = ' b (+')+(-')=- b=-6a a a+ (+')(-')= a=;!; a a=;!;, b=- ab=-;@; 09 5-<7 + æ-, 5-<7(+) 8>- >-;!; <-, 5-<-7(+) 6<- <-, <- >-;!; <- >-;!; (+){+;!;}>0, +;(;+;!;> <0 a +b-<0 a=-, b=-9 ab=6 6 5-<7 + 0% 0% ab 0% 09 --< - æ, --<(-) -5<0, (-5)<0 0<<5 æ <5 <, --<-(-) +-6<0, (-)(+)<0 -<< < -<<, -<<5 -, -, 0,,,, <0 æ0, +-<0 (+)(-)<0 -<< æ0 0 < <0, --<0 (-)(+)<0 -<< <0 -<<0, -<< -5 <6-6< -5<6-6< >0 (-)(-)>0 < > -5<6-5-6<0 (+)(-6)<0 -<<6, -<< <<6 -<< -<< <<6 = + -<0 ( +)( -)<0 +>0 -<0 < -<< 096 [] -6[]+5<0 ([]-)([]-5)<0 ;#;<[]<: : [] []=,,, 5, 6, 7 []= < []= < []= <5 []=7 7 <8 < [] 0 0 <, []=0 0 =0 05

106 RPM <, []= - 0, (-) 0 0 < < <, []= - 0, (-) 0 0 < <,, =0 < a=0, b=, c= a-b+c=0-+= 0 < 0% < 0% < 0% a-b+c 0% 098 = -a+5 =- -a+5>-, -(a+)+8>0 < >b < >b (-)(-b)>0 -(+b)+b>0, a+=+b, 8=b a=5, b= a+b=9 099 = --8 = < <0, (+)(-)<0 -<< 090 =- +p+ =a - +p+>a, -p+(a-)<0 << (-)(-)<0 -+<0, p=, a-= a=6 a-p= 09 a -(a+)+a+>0 a>0 a -(a+)+a+=0 D D =(a+) -a(a+)<0 a -a->0, (a+)(a-)>0 a<- a> a>0 a> a> 09 a + -a a ++a- 0 a<0 a ++a-=0 D D = -a(a-) 0 a -a-æ0, (a+)(a-)æ0 a - aæ a<0 a - a - 09 = +(k+)+ =- +(k+)+>- +k+>0 +k+=0 D D=k - <0, (k-)(k+)<0 -<k< k -, -, -, 0,,, 7 09 m +m+>(+) (m-) +(m-)+>0 m=,0 +0 +=>0 m= m+, m->0 m> (m-) +(m-)+=0 D D =(m-) -(m-)<0 m -5m+<0, (m-)(m-)<0 <m<, <m<, m< 06

107 ~ (n+)-(n+)<0 +(n+)-(n+)=0 D, D =(n+) +(n+) 0 n +8n+ 0, (n+)(n+6) 0-6 n - n -6, -5, -, -, a +>a+ a +(-a)->0 a +(-a)- 0 a<0, a +(-a)-=0 D D=(-a) +8a 0 a +a+ 0, (a+) 0 a= (k+)+k=0 D D=(k+) -6k=0 k -0k+9=0, (k-9)(k-)=0 k=9 k= k 9+= (k+) -(k+)+=0 D k+>0 k>- D =(k+) -(k+)=0 k(k+)=0 k=0 k=-, k= f()<0 <- > f()=a(+)(-) (a<0) f(-)=a(-+)(--)=a(-)(+) f(-)æ0, a(-)(+)æ0 (-)(+) 0 ( a<0) f()>0 -<< f()=a(+)(-) (a<0) f(+)=a(++)(+-) =a(+)(-) f(+) 0, a(+)(-) 0 (+)(-)æ0 ( a<0) - æ;!; - æ;!; 095 f()æ0 - f()=a(+)(-) (a<0) f(009-)=a(009-+)(009--) =a(-0)(-007) f(009-)<0, a(-0)(-007)<0 (-0)(-007)>0 ( a<0) <007 >0 008 f()æ0 - f()<0 <- > f(009-)<0 009-<- 009-> >0 < f()=a +b+c(a>0) f() 0 5 f(-5)=a(-5) +b(-5)+c<0 <-5<5 6<< = a +b+c 0 5 a +b+c=a(-)(-5) (a>0) a(-5) +b(-5)+c =a{(-5)-}{(-5)-5} =a(-6)(-0)<0 (-6)(-0)<0 ( a>0) 6<<0 095 f()=- +-+k f()=-(-) ++k 6 f()æ0 f(6)æ0-6++kæ0 kæ;; ;; k 095 f()= -+a- -<< f()<0 f(-) 0, f() 0 f(-) 0 ++a- 0 a - f() 0 9-+a- 0 a 6, a - a - +k f()= -+a- - 6 =f() 07

108 RPM 0955 f()= +a-a - f()<0 f(-)<0, f()<0 f(-)<0 -a-a <0, a +a-6>0 (a+)(a-)>0 a<- a> f()<0 +a-a <0, a -a-6>0 (a+)(a-)>0 a<- a>, a<- a> a<- a> 0956 f() g() g()-f()æ0 h()=g()-f() h()=(- ++a+)-( +-) =- +a+æ0 =h() - h()æ0 h(-)=h()=a-5æ0 aæ5 a =8 =8-8- æ0, - 0 (-)(+) 0 - = =(8- )+ =- ++8 =-(-) +0 - = M=0, =- m=-8 M-m= =0 =- +-=-(-)(-), -(-)(-)æ0, (-)(-) 0 = = +(- +-) = +- + ={+;#;} -;; ;; f{}=@+a-a@ - a+ - =, = 8 8+= =0 D, D = -( -6)æ0, -6 0 (+)(-) =k =-+k ++ =0 ++(-+k) =0 5 -(k-)+k =0 D, D ={-(k-)} -5k æ0 -k -k+æ0, k +k- 0 (k++'5 )(k+-'5) 0 --'5 k -+'5 (-+'5 )-(--'5 )='5 ' <0 (-)(+)<0 -;$;<< -7+6æ0 (-)(-)æ0 ;#; æ, -;$;< ;#; < -, 0,,, 5 --æ [ --5< æ0 [ --5<0 (+)(-)æ0 -;!; æ (-5)(+)<0 -<<5, -< -;!; <5 -, -,, 08

109 6 ~ æ0, (-)(-)æ0 ;!; æ +<+7 --<0, --<0 (-)(+)<0 -<<, -< ;!; < -a+a-<0 (-)(-a+)<0 a> <<a-, -;;, 5<a- 6 6<a a- 6<a <0, -<<, -( `-)<, +->0 (+)(-)>0 <- > -<< << -æ0, - æ, `-<, --<0 (+)(-)<0 -<< - æ <, <<, --5<0 (+)(-5)<0 -<<;%;, <<;%; (-)(+) 0 - -(k-)+(k+)(k-5)>0 {-(k+)}{-(k-5)}>0 <k-5 >k+, k-5 -, k+ - k M=, m=- M-m=5 k-5 - k (k-)+k =0 D D =(k-) -k <0, -6k+9< (-)(+) 0 - +(k+)-k-<0 (-)(+k+)<0, < -k-> k< >0 (-)(-)>0 < > -(a+)+a 0 (-)(-a) 0, < a >0 (+)(-)>0 <-;!; > - -k- k<- a a k>;#; -k+k=0 D D =(-k) -k<0, k -k<0 k(k-)<0 0<k<, ;#;<k< k, (a-)-a+=0 D D =(a-) -(-a+)æ0 a -æ0, (a+)(a-)æ0 a - aæ +(a+)+a+=0 D D =(a+) -(a+)<0 a -a<0, a(a-)<0 0<a<, a< a, 09

110 RPM 097 +(a-)+a -=0 D D =(a-) -(a -)=0, -a+=0 a= -(b+)+a+b=0, -(b+)++b=0 D D =(b+) -(+b)<0 b -<0, (b-)(b+)<0 -<b< b 0% 0% b 0% 097 -a+a=0 D D =(-a) -aæ0, a -aæ0 a(a-)æ0 a 0 aæ -+-a =0 D D =(-) -(-a )æ0, a -æ0 (a-)(a+)æ0 a - aæ, a 0 aæ -a+a=0 D D =(-a) -a<0, a -a<0 a(a-)<0 0<a< -+-a =0 D D =(-) -(-a )<0, a -<0 (a-)(a+)<0 -<a<, 0<a< a 0 aæ 097 n-5>0, n>0, n+5>0 n>5 n+5<n+(n-5) n>0 (n+5) >n +(n-5), n -0n<0 n(n-0)<0 0<n<0,, 0<n<0 n,,, a a 0.65 a-0.65 a kg (a+0.65)+(a-0.65)=6 a=6 a= 0975 a(a-)(a+)=a +a -6a, a a +a -6a<a,a -6a<0 a(a-6)<0 0<a<6 a->0 a> <a<6 a ++5= 0976 n 000n(0-0.n), n S S=000n(0-0.n)-6000næ n +0000n-6000næ n -000n n -0n+500 0, (n-50)(n-70) 0 50 n f()= -k+ f()=0 =f() f()=0 D D =(-k) -æ0, (k+)(k-)æ0 k - kæ f()>0 -k+>0 k<;%; =f() 0

111 8 ~ 0 f()= -k+=(-k) +-k =k k>,, k<;%; =0 (-)(+)=0 = =- f()= -5+a f()=0 - =f(), f(-) f()<0 (+5+a) (-0+a)<0-6<a<6-6<a< p+p+=0 a, b(a<b) a, b 0<a<b< f()= -p+p+ f()=0 D D =(-p) -(p+)æ0, p -p-æ0 (p-)(p+)æ0 p - pæ f(0)>0 p+>0 p>- f()>0 9-6p+p+>0 p<;; 5 ;; f()= -p+p+ =(-p) -p +p+ =p 0<p< ~ p<;; 5 ;; 0980 f()=a -+a- f()=0-0 f(-) f(0)<0 0 a b f()=a -+a- - 0 a b =f() =f() (a++a-)(a-)<0 a(a-)<0 0<a< - f()=0 f() f()<0 (a-+a-)(9a-6+a-)<0 (5a-6)(5a-)<0 ;5$;<a<;5^;, ;5$;<a<;5^; ' =0 = 5 -' +' >0 -+<0 -+={-;!;}+;*;> >0-6+9<0 (-) <0 -+5=(-) +>0, [ - ++>0 (-)(-) 0 --<0, (-)(+)<0 -<<, < -<-< -<<5 + <5-5<+<5-6<< -<<0 -<-<6 + -6<-<6 ;5$;<a<;5^; 0% - 0 0% 0% a 0% -6<-<6

112 RPM æ0 -+=(-) +æ (-)(+) 0 -, a+a>0 -a+a=0 D, D =(-a) -a<0, a -a<0 a(a-)<0 0<a< <6 <-, -(-)-(+)<6, -<6 >- <- - <, -(-)++<6, -<6 >- - < -<< æ, (-)++<6, -<6 < æ <,, -<< 0, 0987 a(-) b(+) (a-b) a+b a-b=0, a+b<0, b=a a<0 a<0, b<0 b=a a+b>a-b a+8a>a-a, a>-6a <- ( a<0) 0988 g()-f()>0 g()>f(), =g() =f() <- >6 a=-, b=6 a+b= k< -k+k- -(k-)+(k-)>0 -(k-)+(k-)=0 D D=(k-) -(k-)<0 k -6k+5<0, (k-)(k-5)<0 <k<5 a=, b=5 b-a= 0990 f()= +k, f(-)>0, f(0)<0, f()>0 f(-)=+k>0 k>- f(0)=k<0 f()=+k>0 k>-,, -<k< a+b>- -(a+)+b+>0 <- > (+)(-)>0 --6>0 a+=, b+=-6 a=-, b=-8 a+b= f()= -m-m+5 =f(), f()<0 f()=6-m<0 m> m> 099 +k+=0 D D =9k -æ0, (k+)(k-)æ0 k -;@; kæ;@; +k+k=0 D D =k -k<0, k(k-)<0 0<k<, ;@; k< k,, æ0, (-)(-)æ0 æ ,

113 0 ~ 0995 k -+(k-) 0 k -+(k-)>0 k>0 k -+(k-)=0 D D =(-) -k(k-)<0 k -k->0, (k-)(k+)>0 k<- k>, k> k> 0996 k->0, (k-) -(k-)+=0 D, D =(k-) -(k-)=0 k -k+=0, (k-)(k-)=0 k= k= k> k= = =- - æ0, - 0 (+)(-) 0 - =- - - =-(- ) - = +-=(+) - - =-, a-d<0 a<d a=b+c-d (b+c-d)-c>d-b, b-d>d-b b>d b>d, b=a+d-c a-c>d-(a+d-c), a>c a>c,, c<a<d<b > - æ, -->(-) -5>0, (-5)>0 <0 >5 æ >5 <, -->-(-) +-6>0, (+)(-)>0 <- > < <-, <- >5 a ++c<0 <- >5 a<0 <- >5 (+)(-5)>0, --5>0 a a -a-5a<0 ( a<0) a ++c<0 -a=, -5a=c a=-, c=5 a+c= a < -<-a< -+a<<+a 0<< -a < -+a 0, +a 0 a -+a 0 +a 0 a 00 (-)<a(-a-) (-a)<-a -a+ (a-)>(a+)(a-) a= 0 > ( ) >0a->0 (a+)(a-) > =0 a- a +a-=0a-0, a -9a+8=0 (a-)(a-6)=0 a= a=6 a= a=6 >0 () <a-<0 (a+)(a-) < = a- a +a-=a-8, a -a+6=0 a -a+6={a-;#;}+: :>0 a, < () 00 f()<0 <- > f()=a(+)(-) (a<0) f(--)=a(--+)(---) =a(--)(--5) =a(+)(+5) f(--)>0, a(+)(+5)>0 (+)(+5)<0 ( a<0)

114 RPM -5<<- a=-5, b=- ab=0 00 (a+b)-b+a>0 (a+b)>-a+b < a+b<0 -a+b < a+b -a+b, = -a+b=a+b a+b a=b a<0 a<0 (b-a)+a+b>0 (a-a)+a+a>0 -a>-5a >5 ( a<0) >5 a+b<0 0% b=a 0% a<0 0% 0% 00-0 (-) 0 0 +æ6 +-6æ0 (+)(-)æ0 - æ a +b-(a+b)æ0 a +b-(a+b)=0 = = b b - =6 =- a a - 0% +æ6 0% 0% b 0% a 005 a>0 + a -a + a -a- a- +6-(a+)(a-)>0 {+(a+)}{-(a-)}>0 <-a- >a- -a- -a- -a- -a-, a-æa- aæ a [] -[]>0 006 [ [] -[]+ 0 []([]-)>0 []<0 []> ([]-)([]-) 0 [], <[] [] []= < 007 f()>g() a -+>- +a- (a+) -(+a)+>0 a+=0, a=-, >0 a++0, a+-, a- a- + a 0% +6-(a+)(a-)>0 0%, a 0% a 0% < 0% 0% 0%

115 ~ a+>0 a>- (a+) -(+a)+=0 D D =(+a) -(a+)<0 a -<0, (a+)(a-)<0 -<a<, -<a<, - a< - a< 008 " k -k- k -k-<0 k=0,0 +0 -=-<0 k=0 k+0, k<0 k -k-=0 D D =k +k<0, k(k+)<0 -<k<0, -<k<0, -<k <- >5 (+)(-5)>0 --5>0 a +b+c<0 a<0 a a -a-5a<0, b=-a, c=-5a a(-) -b(-)+c>0 a(-) +a(-)-5a>0 (-) +(-)-5<0 ( a<0) -9<0, (-)(+)<0 -<< >0 (-)(-)>0 < > -(a+7)+7a<0 (-a)(-7)<0 a<<7 ( a<7), - a<0 -a a<0 [-] +[]- 0 (n-) +n- 0, n -n+ 0 (n-)(n-) 0 n, [] [] []=, []=, < []=, < < 0 f()= -a+a+ f()=(-a) -a +a+ (a, -a +a+) -<< f()>0 a -, -<< =f() f(-)æ0 a+æ0 aæ- a - a=- -<a<, -<< =f() f(a)>0 -a +a+>0, a -a-<0 (a+)(a-)<0 -<a< -<a< -<a< aæ, -<< =f() f()æ0 -a+7æ0 a ;&; aæ a ;&;,, - a ;&; < - a a -, 0,,, 5 5 a - - a =f{} =f{} =f{} 0 []=n(n n <n+ n- -<n- [-]=n- 5

116 RPM 0 0 AB = 8-(-) =0 0 0 R - = -= =7 = R(7) R() 05 S +5 =5 +5= 5 =0 =-0 S(0) S(-0) 06 B - =7 -= 7 =- =0 B(-) B(0) _8+_(-) 0 p= =0 + _8-_(-) q= =- - p+q=0+(-)= P (, ) _5+_(-) _(-)+_ = =;; 5 ;;, = =- + + P{;; 5 ;;, -} Q (, ) _5-_(-) _(-)-_ = =, = = Q(, -8) M (, ) = -+5 =, = - =-;!; M{, -;!;} P{;; 5 ;;, -} Q(, -8) M{, -;!;} 07 AB =" ( -) +{ 5-(ç-ç) } Ω ='å7 08 AB =" {- (-ç)} +{ - - (-ç)}ω ='å7 'å7 'å7 06 AB (, ) a- +b =, = a=6, b=- ab= A =" +( -5) Ω='å 'å 00 AB =" (-a ) + bω ="a +b "a +b 07 (, ) = +-6 =-, = -+ = (-, ) (-, ) _(-)+_ 0 P{ } P{;; 5 ;;} + Q{ M{ _(-)-_ - - } M() } Q(8) P{;; 5 ;;} Q(8) M() 0 AP = -(-) =5, PB = 5- = AP PB =5 P AB AQ = 7-(-) =9, QB = 5-7 = AQ QB =9 Q AB (, ) a+(-a)+(+a) = = (5-'5)+'5+ = = (, ) (, ) 09 (, -) 5++b a+- =, =- 7+b =, a+ =- a=-5, b= a+b= C (, ) (, ) 6

117 7 ~ =, +6+ = -+ =, 8+ = =7, = C(7, ) C(7, ) 0 AB =5' " (a- ) +( -a )Ω =5' (a-) +(-a) =50 a -6a+=50, a -8a-9=0 (a-9)(a+)=0 a=- a=9 a>0 a=9 0 AB ="{ (- ')ç- } +( -'ç) Ω =" + ' + -' ='6 0 A =AB A =AB a + =(-a) +(-) a +9=a -a+5 a=- a=- 0 AB ="( -a ) + (a+ç)ω AB =" a + a+ 0 AB =" (a+ç)ω ç+ 8 a=-, AB 05 P (a, b) P -=7 a-b=7, P A, B AP =BP (a-) +(b+) =(a-5) +(b-) a -a+b +6b+0=a -0a+b -b+6 8a+8b=6 a+b=, a=, b=- P(, -) P(, -) 06 P (a, 0) AP =BP AP =BP (a-) +(-) =(a+) +(-) a -a+5=a +a+7-6a= a=- P(-, 0), Q (0, b) AQ =BQ AQ =BQ (-) +(b-) = +(b-) b -b+5=b -8b+7 6b= b= Q(0, ) PQ =" + =' 07 AP =BP AP =BP (a-) +(b-) =(a+) +(b-5) a -a+b -6b+0=a +6a+b -0b+ -8a+b= a-b=-6 AP =CP AP =CP (a-) +(b-) =(a+) +(b+) a -a+b -6b+0=a +a+b +b+ -a-8b=-8 a+b=, a=-, b= a-b=- 08 ABC P(, ) AP =BP =CP AP =BP AP =BP (-8) +(-) =(-) +(+) = =-70 +=7 BP =CP BP =CP (-) +(+) =(-6) +(-8) = =90 +=5, =, = P(, ) (, ) 09 AB =(-) +(--) = BC =(-) + =8 CA =(+) + =0 CA =AB +BC ABCB=90 00 AB = +(--) =0 7

118 RPM BC =(-) +(+) =0 CA =(-) +(-) =0 BC =AB +CA, AB =CA ABCA=90 AB =CA 0 A A' A'(-, -) AP =A'P AP +BP =A'P +BP æa'b =" (+ ) +( +ç)ω =5' A(-, ) A'(-, -) B(, ) P ABC=;!;_AB _CA ABC=;!;_'å0_'å0=5 AB 0% BC 0% CA 0% ABC 0% 0 AB =(--a) +(-) =a +a+ AC =(-a) +(-) =a -6a+8 BC =(+) +(-) =0 AB +AC =BC (a +a+)+(a -6a+8)=0 a -a=0, a(a-)=0 a>0 a= 5 0 AB =(-a) BC =(-) +(b-a) =+(b-a) AC =(-a) +(b-a) =a -a++(b-a) ABC BC =AC, =a -a+, a -a+=0 (a-)(a-)=0 a= a=, a= AB = a= AB =0, '= 05 AB ="( + ) + (5-ç)Ω =5 AP +BP, APB B(, 5) A A' A(-, ) A'(-, -) AP =A'P AP +BP =A'P +BP AP +BP æa'b AP +BP ="( + ) + (5 +)Ω ='6å5 AP +BP '6å5 ABC 5+'6å5 06 A A' A'(-, ) B B' B'(6, -5) AP =A'P, BQ =B'Q AP +PQ +QB =A'P +PQ +B'Q AP +PQ +QB æa'b' A'(-, -) AP +PQ +QB ="( 6+ ) + (-5 -)Ω ='ßå AP +PQ +QB 'ßå 'ßå 07 PA +PB +PC =(-) +(-6) + +(-) +(-) +(+) = =(-) +(-) +0 =, =, 0 A'(-, ) A(, ) P Q P B(6, 5) B'(6, -5) 0 B(, ) B' B'(-, ) BP =B'P AP +BP =AP +B'P AP +BPæAB' AP +BP="( + ) + (-ç) Ω='å B'(-, ) B(, ) P A(, ) 08 P (, ) PA +PB =(-) +(-) +(-) +(-6) = =(-) +(-) +0 =, =, 0 P (, ) 8

119 9 ~ 09 P +PA +PB =a +b +(a-5) +(b-) +(a-) +(b-9) =a -8a+b -b+ =(a-) +(b-) +56 a=, b=, m=56 a+b+m=6 6 AM 60% '7 GM 0% 050 ABC A(, ), B(, ), C(, ), P(, ) PA +PB +PC =(- ) +(- ) +(- ) +(- ) +(- ) +(- ) = -( + + ) ( + + ) ={- } + + +{- } ( + + ) ( + + ) =, =, PA +PB +PC PABC 05 MBC AB +AC =(AM +BM ) 6 + =(AM + ) 6=AM +6, AM =0 AM ='å0 ( AM >0) 05 C (c, 0) AB +AC =(a+c) +b +(a-c) +b =a +b +c AB +AC = (a +b +c ) AB +AC =(AM +BM ) 'å0 05 A D M ABD 8 M 8 8 AB +AD =(AM +BM ) 8 + =(AM +8 ) 0=AM +6, AM =0 B C AM ='å0 ( AM >0) AC =AM ='å0 055 P (a, b) _(-)+_5 _+_(-) a= =, b= =- + + P(, -) Q (c, d) _(-)-_5 _-_(-) c= =, d= = Q(, -5) 'å0 PQ {, }=(7, -) 056 B (a, b) AB { _a+_, _b+_ }={;5&;, ;; 5 ;;} + + a+=7, b+6= a=, b= B (, ) (, ) 05 BM =CM AB +AC =(AM +BM ) 8 +('6) =(AM + ) =AM +6, AM =8 AM ='7 ( AM >0), G ABC GM =;!; AM GM=;!;_'7= '7 057 AB (+t) t (+t)_+t_ (+t)_a+t_(-) {, } +t+t +t+t +5t a+(a-)t ={, }=(, ) +t +t +5t a+(a-)t =, = +t +t t=, a=6 058 AB =BC AB BC = C AB 9

120 RPM C _-_(-) _-_ {, }=(5, 8) a>0 AB A, B, C AB =BC AB BC = C AB 5 C 5_5-_(-) 5_-_0 {, }=(, 5) 5-5- a=, b=5 a+b=9 060 AB k 5 k_-5_(-) k_-5_ k+5 k-5 {, }={, } k-5 k-5 k-5 k-5 ++=0 k+5 k-5 + +=0 k-5 k-5 0k-0=0 k= 06 AB _(b+)+ (-)+_(a+) {, }=(, ) + + b+ a-, =, = a=, b= B(, -), C(, ) BC _- -_(-) {, }=(, ) - - =5, =8 - = a, b 0% B, C 0% BC 0% - 0% 06 A(, -), B(-, 6) AB k (-k) k_(-)+(-k)_ k_6+(-k)_(-) {, } k+(-k) k+(-k) -5k 9k-6 ={, } -5k <0, 9k-6 >0-5k 9k-6 <0 k> >0 k> k>0, -k>0 0<k<,, <k< <k< AB m n m>0, n>0 06 AB =" (- -) ç+ (-8 -)Ω = AC ="( 5- ) +( - )Ω =5 AD A AB AC =BD DC 5 BD DC =AB AC = 5 D BC 5 D _5+5_(-) _+5_(-8) {, }={;%;, -;#;} AB =" + (-ç)ω =5 AC =" (-5 ) + (-8 -)Ω = AD A AB AC =BD DC BD DC =AB AC =5 {;%;, -;#;} D BC 5 D 5_(-5)+_ 5_(-8)+_ {, }={;#;, -;#;} a=;#;, b=-;#; a-b=_;#;-_{-;#;}=6 065 AD A AB AC =BD DC = AB =a, AC =a (a>0) ABC 0

121 ~ 6a =9a +7, 7a =9 a =7 a='7 ( a>0) AC =a='7 '7 066 AD A AB AC =BD DC = AB =AC AB =(-a) +(-) =a -a+0 AC =(8-a) +(-) =a -6a+80, a -a+0=a -6a+80, a=70 a= ABC (, -) a-b- =, b++5 =- a-b-= a-b=5 b++5=-6 b=-5, a=-0, b=-5 a+b=-5 a=-8, b= B(-8, ) ABC (0, ) -8+c =0, ++d = c=, d=- C(, -) BC ="( +8 ) + (- - )Ω =' 7 07 B, C (a, b), (c, d) BC (0, ) a+c =0, b+d = a+c=0, b+d=8 ABC (, ) +a+c =, +b+d = =, =;; º;; +=;; ;; 068 C (a, b)abc (-, 0) -5+a =-, -5++b =0-5+a=-9 a=-8-5++b=0 b= C (-8, ) 069 ABC a+b- =0, +6+ab =0 a+b=, ab=-7 a +b =(a+b) -ab = - (-7)=0 070 AB (8, ) 0+a+c =8, 0+b+d = a+c=, b+d= AB { a+c, b+d }={;; ;;, ;; ;;}=(, 6) (, 6) 07 B, C (a, b), (c, d) AB (-, ) +a =-, +b = 07 A(a, a ), B(b, b ), C(c, c ) AB, BC, CA P(, 0), Q(, 5), R(-, ) a +b a +b =, =0 a +b =, a +b =0 b +c b +c =, =5 b +c =6, b +c =0 a +c a +c =-, = a +c =-, a +c =,, (a +b +c )=8, (a +b +c )= a +b +c =, a +b +c =6 ABC a +b +c a +b +c {, }={;$;, ;^;}={;$;, } a=;$;, b= a-b= 07 ABC A(, ), B(, ), C(, ) ABC G G{, }

122 RPM AB, BC, CA P, Q, R B(, ) P + + P{, } Q{, } R{, } + + PQR G' A(, ) + + = G' G'{, }, G G' 075 D (, ) AC BD -+ = 0+, + = 0+ =, =5 D (, 5) Q = R C(, ) ABCD AC BD, a+ + +b + {, }={, } b=a+, AB =BC "( -a ) + ( -)Ω ="( - ) + ( - ) Ω a -a+=0, (a-)(a-)=0 a= a= a=, b= a=, b=5 ab AB P _+_8 _+_(-) {, }=(6, -) + + AB Q _-_8 _-_(-) {, }=(8, -) - - PQ {, }=(, -8) 080 AB 5 (n, -5) 5_-_ 5_m-_5 n=, -5= 5-5- m=, n=7 m+n=0 076 AC { a+b, + }=(-, ) a+b=- BD { -, +c }=(-, ) c=5 a+b+c=-+5= 077 ABCD BD AC +a 5+b {, }=(, ) a=5, b=- a+b= 08 AB ='5 "( -ç- a) +( -)Ω ='5 (--a) +=0, a +a-=0 (a+6)(a-)=0 a=-6 a= a>0 a= 08 P (a, 0) AP =BP "( a+ ) + ( -)Ω ="( a- ) + ( -) Ω a +6a+=a -a+7 8a= a=;!; P {;!;, 0}

123 ~ 5 08 AB =(+) +(+) = BC =(-) +(0-) =7 CA =(--) +(-) =7 AB =BC +CA, BC =CA ABCC=90 BC =CA 08 P(a, b) =-+ b=-a+, AP =BP AP =BP a +(b-) =(a-) +(b-) a +b -b+=a -8a+b -6b+5 8a+b= a+b=6, a=-, b=0 ab= ABC ABC m n (m>0, n>0) ABC {, }=(, ) 086 B, C (b, b ), (c, c ) AB M (, ) +b -+b =, = b =5, b =6 B(5, 6), CM ABC _+_c _+_c {, }={;$;, } + + c =-, c = C(-, ) BC (a, b) _(-)+_5 a= =- + _+_6 b= =;; º;; + a+b=;&; 5_-_(-) 5_-_(-) {, }={;; ª;;, ;&;} 5-5- a-b= 088 AC BD M ABD BD, BM =;!; BD ='6 AB +AD =(AM +BM ) 6 +8 =(AM +) AM =6 AM ='å6 ( AM >0) 089 G ABC M BC, AG GM =, GM =" AG =" AM =AG +GM =", BM =;!;BC = AB +AC =(AM +BM ) 6 +AC ={(") + } 6+AC =5, AC =8 AC =" ( AC >0) 090 ABCD AC BD, { +, - }={ -+b, a+c } b=6, a+c=0, AB =AD " (- - ) + (a-ç)ω ="( 6- ) +(c -)Ω a -a+=c -c+9 a -c -a+c=6 (a+c)(a-c)-(a-c)=6 (a-c)(a+c-)=6 a-c=- ( a+c=0), a=-, c= abc=- 087 a>0 AB A, B, C AB =BC AB BC = C AB 5 C 09 AC BD c+d -5 BD {, }, { c+d,-}, =-

124 RPM c+d -=- c+d= a- b- AC {, }, BD (, -) a- b- =, =- a=, b= a+b+c+d=8 09 A B AB _5+_(-) _+_(-) {, }=(-, -) + + B C BC _(-)+_5 _+_ {, }=(, ) + + (-, -) (, ) _+_(-) _+_(-) {, } + + ={;!;, -;!;} +7 a+b a+b {, }={, } ab a+b {,} {, } ab = ab=8 a+b = a+b=6 a +b =(a+b) -ab(a+b) =6-8 6=7 096 AB t (-t) t_(-6)+(-t)_ t_5+(-t)_(-) {, } t+-t t+-t =(-8t+, 9t-) (-8t+, 9t-) -8t+<0, 9t-<0 t>0, -t>0 0<t<, <t< <t< AB A =B =AB A =B A =B +0 =a +(') a = a=- a= A =AB A =AB +0 =(a-) +(') a -a+=0, (a-)(a-)=0 a= a=, a 09 A(-, 0), B(0, 7) AB k _0+k_(-) _7+k_0 -k 7 {, }={, } +k +k +k +k += -k +k +_ 7 +k k= k= =, -k+=(+k) 095 ABCD AC 0+ab 5+ ab {, }={,} BD 097 ABC P(a, b) ()=AP =BP =CP AP =BP AP =BP (a-7) +(b-) =(a-5) +(b+) a -a+b -b+50=a -0a+b +6b+ a+b= AP =CP AP =CP (a-7) +(b-) =(a+) +(b-5) a -a+b -b+50=a +a+b -0b+6 a-b= a=, b= P(, ) AP AP ="( -7 ) + ( -)Ω = P(a, b) A(, ), B(, ), C(-, ) PA +PB +PC =(a-) +(b-) +(a-) +(b-) +(a+) +(b-) =a -6a+b -b+5 =(a-) +(b-) +0 a, b (a-) æ0, (b-) æ0

125 5 ~ 7 a=, b=, P(, ), PA +PB +PC 0 P(, ), ABN AB +AN =(AM +BM ) +AN =(AM +5 ) AM -AN =9 AMC AM +AC =(AN +MN ) AM +9 =(AN +5 ) AN -AM = + AM +AN =5 00 = A = A' AP +BP A' P A'B A B A'(0, ) AP +BP 6 A'B ="( 0-6) +( -0Ω) ="5Ω="Ω 0 AB =" (- 8- ) + (- -ç0 ) Ω =6 AC ="( 0- ) +( -ç0)ω =0 AD A AB AC =BD DC BD DC =AB AC =6 0= 5 DBC 5 D _0+5_(-8) _+5_(-) {, }=(5, -) D(5, -) -5t-<0, t->0 t> t> 50% t 50% 0 D (a, b) AC BD +k + +a +b {, }={, } +k +a =, = b=0, k=a+, ABCD 6"5 AB +AD ="5 "( - ) + ( -) Ω +"( a- ) +(b -) Ω="5 "a - 6a +="5 ( b=0) a -6a-7=0, (a+)(a-7)=0 a=- a=7 D(-, 0) D(7, 0) +b a=-, k=-+=0 a=7, k=7+=8 k 0 8 0, 8 AC BD 0% D 50% k 0% AB 0% AC 0% BD DC 0% D 0% 0 AB (t+) t (t+)_(-)-t_ (t+)_(-)-t_(-) {, } t+-t t+-t =(-5t-, t-) 0 PA +PC æp'a +P'C PB +PD æp'b +P'D P AC BD D(0, 5) C(, 5) P', PA +PB +PC +PD (A) B(, 0) P P P' 5

126 RPM { 0+, 0+5 }={;#;, ;%;} 05 P (, ), A (-, -), B (, ) "( + ) + ( +)Ω +"( - ) + ( - ) Ω =AP +BP æab ="( + ) + ( +)Ω = B =A = A(, 0) E E(a, 0) C(a, ) CD =CE 0-a= a=7 {;#;, ;%;} PA +PB +PC +PD 60% P 0% A(, 0), C(7, ) A, C AC =" (7- ) + Ω=" 7Ω8 07 D BC DBC C (c, 0) B (-c, 0), A (a, b) AB =(-c-a) +(-b) =a +b +c +ac AC =(c-a) +(-b) =a +b +c -ac AD =a +b DC =c AB +AC =(a +b +c +ac)+(a +b +c -ac) =a +b +6c =(a +b +c ) =(AD +DC ) " 7Ω8 A(a, b) B(-c, 0) (D) C(c, 0) k= B{0,} - - A{-,-} C{a,} A{,0} E{a,0} B{,} P{,} D{0,} 0 08 d(p, Q)=5 P, Q P(0, 0), Q(5, 0) P Q _5+_0 {, 0}=(, 0) + P Q _5-_0 {, 0}=(-0, 0) - P Q, P Q d(p Q, P Q)="( -0 -) Ω ç+ 0 d(p Q, P Q)= 09 A(-a), B(0), C(a) (a>0), P() AP +BP +CP =(+a) + +(-a) AP +BP +CP = +a+5a AP +BP +CP ={+;!;a} +;; ;;a =-;!;a,ap +BP +CP AP = -;!;a-(-a) =;%;a BP = -;!;a-0 =;!;a AP BP =5 AB 5 0 A(, 8), B(8, ), A A', B B' A'(-, 8), B'(8, -) A'(-, 8) P A(, 8) Q AP =A'P, QB =QB' AP +PQ +QB =A'P +PQ +QB' æa'b' l='6ßå8 ="( 8+ ) +( - -8) Ω ='6ßå8 B(8, ) B'(8, -) l =

127 7 ~ 9 (-)+ =0+=0, -=0, -(-)=(-) =- =- 0 a=-;!; + = =+6 =+6-6 = = -- -= {-(-)} -(-) 5+-=0 5 -= -- (-) - = =0 =-+9 6 = = 7 =-;ba;-;bc; (, b+0) a>0, b>0, c<0 -;ba;<0, -;bc;>0,,, =-;ba;-;bc; (, b+0) ab<0, ;bc;<0 -;ba;>0, -;bc;>0,, b=0 a+c=0 =-;ac; a>0, c<0 -;ac;>0, -;ac;>0,,,,,, 8 +-=0 =-+ ++=0 =-- --6=0 =+6 +-=0, 9 (-)_=- =-+, =-, {-;!;} a=- a= -;!; = a + a- a -a=, a -a-=0 (a+)(a-)=0 a=- a= a+ a=- a= (a-)+a =0 a=;!; ++=0 =-;#;-;!; - ;!; -;#; (, -) -(-)=-;#;(-) =-;#; =-;#; =-+ ;!; -=;!;(+) =;!;+;%; =;!;+;%; (+5+)+k(++)=0 k +5+=0, ++=0 =-, = (-, ) (-, ) 5 k (+-)+k(-+)=0 k 7

128 RPM +-=0, -+=0 =;5!;, =;5#; {;5!;, ;5#;} {;5!;, ;5#;} 6 (--)+k(-+)=0 -+k=0 k= k= --+-+=0-7=0-7=0 - + " +( -)Ω 5 '5 7 = ='5 '5 - (-5)+ 6 8 = ='å 'å " +( -) Ω 'å 6 9 =;5^; ;5^; " +( -)Ω ' ' += (-') = - 5 ( )=tan 5 = - =- =(m-)-n- m-=, -n-=- m=, n= m+n=5 5 6 A(6, -), B(, ) AB _+_6 _+_(-) {, }=(, -) + +, (, -), (-, ) -(-) -(-)= (-) = (-, ), (, -) -- -= (+) =-+ -(-) a=-, b= a+b=0 0 =- (0, -) =+, -+=0 + 6 = =' ' " +( -)Ω ' +-=0 (0, ) ++=0 + " + '5 = = '5 5 '5 5 =+b -, (-, 0) 0=-6+b b=6 =+6 8 +=-, -=-0 (-, ) (-, ), (, 0) 0- -= (+) -(-) =-;@;+ =-;@;+ 9 A(, 5), B(, 8) 8-5 = - (-, -) +=(+) =+ =+ (-, ), (6, 8), { -+6, +8 }=(, 5) - -5=-(-) =-+7 = =k ;K;, ;K; ;!; ;K; ;K;=, k =6 k=6 ( k>0) k ;; k ;; ' ( )=tan 0 = (', -) - + = - 8

129 9 ~ 5 (-, a) - a + = a= = a, b a b a>0, b>0 b 9 a ;!;ab=9 ab=8 8 A, B, C AB BC ( AB)= -5 = --k k+ ( BC)= -- = -k-(-) k-, =, k-=k+ k+ k- k=- A(, ), B(a, 5), C(, a+)l AB AC, 5- (a+)- =, =a a- - a- =a -a, a -a-=0 (a+)(a-)=0 a= ( a>0) l A(, ) l -=(-) =+ -;!;, -;!; 5 =m+a(0, ), ABC BC M{ +, + }, M{;%;, ;%;} A C -;!; AB AC 0% a 0% 0% =m+ M B M =m+ ;%;=;%;m+ m=-;5!; -;5!; 6 ;{;+;};= A(, 0), B(0, ) AB =m AB M(, ) m= 7 BC BC M 5+(-) -5+ {, }=(, -) A(, ), M(, -) -= -- - =5- (-) a=5, b=- a +b =5 +(-) =69 8 A, B A{ -, - }, A(-, -) B{ +, +5 }, B(, ) - A 69 A, B -(-) += (+) -(-) =+ - B A 5 M B =m BC 0% 50% a +b 0% 9

130 RPM 9 a+b+c=0 =-;ba;-;bc; ab<0, bc<0 ;ba;<0, ;bc;<0 -;ba;>0, -;bc;>0, 5 A{;(;, 0}, B(0, ) =-;$; m {-;$;} m=- m=;#; ;#; (6, 0) =;#;(-6), =;#;-;(; --8=0 50 bc=0 b=0 c=0 ab<0 c=0 a+b+c=0 =-;ba; ab<0 ;ba;<0 -;ba;>0,, 5 +a+b=0 =-;a#;-;ab;,,, -;a#;>0, -;ab;<0 a<0, b<0 a+b+=0, =-;ba;-;b@;,,, 5 a+b-=0, =-;ba;+;b@; -;ba;<0, ;b@;<0 a<0, b<0 -+a-b=0 =;a!;+;ab;, 5 +(a-)+a-=0, (a-)-+a+=0 (a-)+(a-) (-)=0 a-=0 a= 55 -a+=0 +(b-)-=0 -a ;!;= + a+b= b- - -a+=0 (a+)-(b-)+=0 (a+)-a(-b+)=0 ab=- a +b =(a+b) -ab = - (-)=6 56, a+ - a = + -a a +a-=0, (a+)(a-)=0 a=- ( a +), a+ - a = = a= -a, (a+)+a=0 a=- a=-, b=, c=- ab c 0% 0% a +b 0% 6 (-) = = - 0

131 5 ~ 5 57 A(, ), B(-, 5) 5- =-;!; -- AB, AB AB (-, ) -=(+) =+6 58 A(, ), B(0, -) -- = 0- AB -, AB AB (, ) -=-(-) =-+ m=-, n= mn= A(-, ), B(, 5) 5- =;!; -(-) AB -, AB AB (0, ) =-+ (a, b) b=-a+ a+b= 60 A(a, ), B(, 5) AB =-+b 5- -a _(-)=- a= =-+b AB { a+, +5 }=(, ) =-+b b=7 a+b=9 6 +=0 -+=0 a++a+=0, a a+ = + a=- -, = + 0 a=;!; a a+, =-, = (-, ), -a++a+=0 a=,, a -+;!;+=;#; 6 k+=-7+=8, +=5 +=8 +=5 =, =- (, -) k+=-7(, -) k-=-7 k= =0 --=0 a+-=0,, -;!;, ;$;, -a,, {-;!;} (-a)=- a=-, ;$; (-a)=- a=;#;, a -+;#;=-;%; -;%; 6 a++5=0 =-a-5 +b-=0 =- + b b ++=0 =-;!;-;#;, -a=-;b@;=-;!;, ;b$;+-5, ;b$;+-;#; a=;!;, b= a+b=;(; ;(; k

132 RPM k k k 65 A C(, 6) BC E, E C AB D AB -0 =;!; 7- CD - A(, 0) B(7, ) D C(, 6) - -6=-(-) =-+5, BC -6 =- 7- AE A(, 0) =-, =, = (, ) 66 B(, 8) A BC D D BC 8-b (, ) C(a, b) -a A(-, 0), AD -0 = -(-) 8-b _=-, 8-b=-+a -a a+b= (k+)-(k-)-5k-=0 k (--5)k+(+-)=0 k --5=0, +-=0 =, =, (, ) a=, b= ab= 68 m+m+-=0 m m(+)+(-)=0 m +=0, -=0 =-, =, P(-, ) P ="( -) + = =0, +-=0 --+k(+-)=0 (, ) --k=0 k=- k=- ---(+-)=0-5+5=0 -=0 a=0, b= a+b= 70 ++=0, --=0 (++)+k(--)=0 (+k)+(-k)+-k=0 ++=0 +k = -k + +k=-k k=;!; k=;!; ;^;+;#;+;#;=0 ++=0 a=, b= a+b= =0, +5-= k(+5-)=0 (k+5)+(5k+5)-k+=0 --=0 (k+5) +(5k+5) (-)=0 -k-0=0 k=-;%; -k ;%;+;%;+;; ª;;= = =0 7 a+(a+)+=0, (a-6)+a-=0 a+(a+)++k{(a-6)+a-}=0

133 5 ~ 55 -k=0 k= (a-6)+(a+)=0 a-6 - =, -a+6=a+ a+ a=;@; ;@; B(-, ), -k-=0 k=-;!;, k -;!; k k +{-;!;}=;#; ;#; 7 m--m+=0 m(-)-(-)=0 m (, ) (, 0), -m+=0 m=;#; (0, ), -m+=0 m=;!;, m ;!;<m<;#; ;!;<m<;#; 7 =m(-)+ m (, ) A, B A(, ), =m+ m=;!; B(5, -), -=m+ m=- B, A, B m -<m<;!; a=-, b=;!; a+b=-;!; 75 k--k+=0 k(-)-(-)=0 k (, ) B AB A(, 0), -k+=0 k= - A - A +-= =a+-a a(-)+(-)=0 a (, ) - (æ0) = =[ - (<0) = a=, =- a=- =- = a -<a< 77 k (+-)+(-)k=0 k +-=0, -=0 =, = A(, ) A(, ) -+b=0 '5 -+b ='5, +b =5 " +( -) Ω b= b=-6 b A(-, ), B(, ) - -= (+) -(-) +-=0 C(, ) '5 = = " + ' =0 =;#;+ m ;#; m=- m=-;$; =-;$;+a, +-a=0

134 RPM -a =, -a =5 " + -a= 5 a=-5 a=5 a =5 5 8 P(, ) (0, 0) P P ;@; P(, ) 80 (a, )-+=0, +-=0 a-+ " çç+ ( -)Ω = a- = a+5, a-= (a+5) a=7 a=- a+6- " + a>0 a= k(+)=0 (k+)+(k-)-=0 (, -) f(k) (k+)+(k-) (-)- f(k)= "( k+ ) +( k-ç)ω = "5 k +Ω5 " 5k ç+ω5, k=0f(k) '5 f(0)= = ' =0, -=0 +++k(-)=0 (k+)+(-k)+=0 = "( k+ ) +( -k)ω "5 k + k+ω "5 k + k+ω, 5k +k+=5{k+;5!;} +;5(;æ;5(; '5 k=-;5!;, = Æ;5(; =, = =: ;5@0);º:=(m) " 0 +ç0ω '5 -;#; -;#; 85 ++=0 (-, 0) ++k=0 -+0+k ='5, k- =0 " + k-= 0 k= k=-9 k 86 -+=0 (0, ) --=0 -- = =' " +( -) Ω ' 87 a+-=0, +(a-)-=0 ;A;= + - a(a-)=6 a- - a -a-6=0, (a+)(a-)=0 a=- a= a= a=- a=-, -+=0, --=0 -+=0 {0, ;!;} --=0 -;#;- 5' = " + (- ) Ω =0, +a-=0 ;!;= a=- a - --=0 (0, -) -+7= = =' " +( -) Ω ' ABCD ' (') =

135 55 ~ P(, ) P ++ " + = ++ = -- ++= (--) --=0 +-=0, 90 P(, ) P ++ " + Ω = ++ = ++ ++= (++) -+=0 ++=0 -+=0 9 (, a) -a+ " +( -) Ω = -- " +( -) Ω ++ " + Ω -a = 5-a, -a= (5-a) a=-;!; a=;(; 9-a- " +( -) Ω a ;&; ;&; 9 A(, ), B(-, -) AB ="( - -) +( - -) Ω =' AB A -(-) += (+) -(-) - =+ B -+=0 - C(a, -) AB d a++ +a d= = " +( -) Ω ' ABC 6 +a ;!; AB d=6, ;!; ' =6 ' +a =8, +a= 8 a= a=- a 95 A -+=0 ;!; AP A -+=0 A =" +ΩΩ ='å7, -+=0 " +( -)Ω = 'å7 AP=;!; 'å7 =6 6 'å7 C(a, -) 9 (, ) ++a " +Ω = 7+a =, 7+a= a=-5 a=-9 a BC ="( - ) +( -0)Ω =' BC -+ " +( -)Ω -0= -0 (-), =- - --=0 A(, ) d -- ' d= = = " +( -)Ω ' ' ABC=;!; BC d=;!; ' = B(, 0) A(, ) C(, ) 96 --=0 +5-9=0 -+6=0 A(, ), C(-, -) =, =, =-, =, =-, =- A(, ), B(-, ), C(-, -) AC AC ="( + ) +( +)Ω ='5, B(-, ) = " +( -)Ω '5 B(-, ) 5

136 RPM 7 ;!; '5 =;; ;; '5 ;; ;; -0 ( AB)= = - 6- ( BC)= = - A, B, C 0% 0% 0% 0% 97 (, a) -a=(-) (a, 6) 6-a=(a-), 6-a=a-6 a= a= =- 98 =- (-, -) +=(+) =+ a=, b= a-b= 99 a-+=0, (a-)++=0 a(a-)+(-) =0 a -a-8=0, (a-)(a+)=0 a=- a= a -+= 0 A(-, ), B(, ) - =-;!; -(-) AB, AB AB { -+, + }=(-, ) AB -=(+) -+5=0 0 k<0 ;{;+;k};=, 6 ;!;_ k _=6, k = k=- ( k<0) 0 a+b+c=0 =-;ba;-;bc; ab<0 ;ba;<0 -;ba;>0 bc>0 ;bc;>0 -;bc;<0,,, k 00 A(-, 5), B(, 9), C(, 5) 9-5 ( AB)= =;$; -(-) 5-9 ( BC)= = - A, B, C A(, -), B(, -5), C(, -7) -5-(-) ( AB)= = (-5) ( BC)= =- - A, B, C A(, 0), B(, ), C(, 6) 0 A(, ), B(a, -), C(a+, 5), D(b, a+9) AB, BC, AD, -- a- -6 a- 5-(-) = = (a+)-a == a+7 b- -6=a- a=- b-=a+7 b-=6 b= a+b= (a+9)- b- 6

137 57 ~ a++=0, -+=0, a = +;!; a=-;!; -, a-=0 a=, p=-;!;, q= pq=- 0 A ABC BC M{ +, 5- }, M(, ) A(, ), M(, ) - C -= - (-) =-;!;+;%; - 5 A M B 06 +=8 (0, ) +=k, +-k=0 -k =, 8-k =0 " + 8-k= 0 k=- k=8 k 6 07 B (a, b) AB A(, ) +-=0 b- _{-;!;}=- a- B(a, b) +-=0 a-b=, +-=0 AB { a+, b+ } a+ + b+ -=0 a+b=0, a=;5@;, b=-;5!; B{;5@;, -;5!;} 08 a++=0+=0, -+=0 +=0, -+=0 =-;#;, =;!; a++=0{-;#;, ;!;} -;#;a+;@;+=0 a= k-(-)-k+ 09 f(k)= = " k + Ω(- )Ω " k +Ω " k +Ω, k=0f(k) f(0)= (a+)-(a-)+a-5=0 a (-+)a++-5=0 a -+=0, +-5=0 =, = A(, ) A(, ) -+p=0 '5 6-+p ='5, +p =5 " + (- )Ω +p= 5 p= p=-7 p - - m-+m-=0 (+)m-(+)=0 m (-, -) (, 0), - m-=0 m=;!; (0, -), m=0 m=0, m 0<m<;!; A(, 5), B(, ), C(, ), D(, 5) ABCD ABCD M M{ +, 5+ }, M(, ) P(-, ), M(, ) - -= (+), =;!;+;%; -(-) -+5= =0 - A D M P B C 7

138 RPM (+-)+k(--)=0 (k+)+(-k)-k-=0 (5, ) 5(k+)+(-k)-k- = "( k+ ) + (-çk) Ω k+5 =, k+5 =" k + " k + 7k -0k-7=0, (k+)(7k-7)=0 k+- k=;; 7 ;; ;; 7 ;;-;; 7º;;-;; 7 ;;=0-5-9=0 (0, ), m-=0 m= (, 0), m+=0 m=-;!;, m-;!;<m< a+b= {-;!;}+=0 8 (k-)+-=0, k-+=0 k- k = = { --, -- }={-, -;%;} { +, + }=(, ) {-, -;%;}, (, ) -{-;%;} +;%;= (+) -(-) =;8(;-;!; a=;8(;, b=-;!; a+b=;8&; ;8&; 6 P(, ) P +- " +Ω = +- = ++ +-= (++) -+=0 +=0 c+0 -+=0 a=, b=-, c= a+b+c= ++ " +Ω 7 =m+m+ m(+)+(-)=0 m (-, ) k-=-k k=;!; -6+=0 -+=0 (0, ) -+ 0 '5 = = " + (-ç6)ω '5 9 -+a=0++=0, -+=0 ++=0, -+=0 =-, =- (-, -) -+a=0(-, -) -- (-)+a+0 a =0, -+=0, +=, -=- ( ) k= (+-)+(-+)=0 7+=0 =-;7!; =-;7!;() (+-)+k(-+)=0 (k+)+(-k+)+k-=0 -k+=0, k= =-;7!; ( ), 8

139 60 ~ 6 -+a=0 -+=0 --a=0, =a-, =a- (a-, a-) (a-, a-) (a-)-(a-)-a=0 -a-=0 a=-;!; -;!; --=0 A(, 5) d -5-5 d= = ='5 " +( -)Ω '5 ABC=;!; BC d ABC=;!; '5 '5=;%; ;%; 0% 0% 0% 0% 0% 0% a 0% a+b=6 ;a^;, ;b^; ;!; ;a^; ;b^;=6 ab=, 0% 0% ab 0% 6 ;b; 6 ;a; AB CD CD -;!; a=-;!; CD =-;!;+b, +-b=0 AB =" + ='5 A(, 0) '5, -b ='5, -b =5 " + -b= 5 b=;&; ( b>0) a+b=-;!;+;&;= CD 0% A CD 0% a+b 0% B(, ), C(, ) BC ="( - ) + (-ç)ω ='5 BC -= - (-), = =0 (a, b) a-b-=0 A(, ), (a, b) M(', ') '= a+, '= b+ a='-, b='- 9

140 RPM ('-)-('-)-=0 6'-8'-=0, '-'-6=0 --6=0 6 A C BC E E D BC 0- A B =- - AE =, B AC D AC BD -;!; BD =-;!;(-) =-;!;+;#;, =, = (, ) a=, b= a+b= 7 AB=90 AB= BC ABC=90, l l, l ;#; l -;@; 9 0 (, ), 5 (0, ), + -=0 (-) + = (, 0), (, 0), =0 (-) +(-) = (, ), (, ), (, ) (-) +(-) = (, -) (-) +(+) = 5 + =9 l =-;@;+, +-9=0 8 B =;!; =a AB P, Q A P B Q 8 =a 6 (-) +(+) =5 7 r (+) +(-) =r (-, 0) +(-) =r r =5 (+) +(-) =5 (+) +(-) =5 P(a, ), Q{a, ;!;a} PQB=;!; BP PQ =;!;(8-a){-;!;a} =;8!;(8-a) PQB=;!; AB ;8!;(8-a) =;!; {;!; 6 } 8 + +A+B+C=0 +5+A+5B+C=0 +6-A-B+C= A+B+C=0 A=-, B=0, C=- + --=0 + --=0 (8-a) =, 8-a= '6 0<a<8 a=8-'6 8-'6 9 0

141 6 ~ 6 (+) +(-) =9 0 (-) +(+) =6, (+) +(+) = + --( )=0 6+8-= =0 D D =6-5 8=-< =-+ + =6 +(-+) =6 -=0 D D =(-) =>0 (-) +(-) = = ( )=0 8+-0=0 +-5=0 + -+k( + -)=0 (, k+-) (, ) +9-+k(+9-)=0 9k+=0 k=k= ( + -)= = = = =0 =-;#;-;; ;; =-;#;-: : + =5 +{-;#;-: :} =5 +6+9=0 D D = -9=0 6 =+ + = +(+) = 8 +=0 =-;$; =-;$; + -++=0 +{-;$;}-+{-;$;}+= =0 D D =(-0) -5 6=0 9 = '5" += '= =+5 =-5 5 r (, -) (-) +(+) =r r =0 + -a+a+a=0 a= a=0-r =0-r r=' ( r>0) ' ' =0 {-;!;} +(+) ={;!;} ;!;

142 RPM 5 r(-, ) (+) +(-) =r (, ) (+) +(-) =r r =8 (+) +(-) =8 5 (a, b) =- b=a- (-a) +(-a+) =r (, ), (, ) (-a) +(-a+) =r 5a -a+0=r (-a) +(-a+) =r 5a -8a+8=r, a=, r = a=, b=, r=' ( r>0) a+b+r=5+' k+0=0 (+) +(-) =-k -k>0 k< k =0 (+) + = =0 (+) +(-) = =0 {+;!;}+{+;!;}=-;!; -;!;< =0 (+) +(+) = + -+=0 (-) +(+) = k-5k -6k-=0 (+k) + =6k +6k+ 6k +6k+, k +k 0 k(k+) 0 - k 0 5+' a -a-=0 (-) + =-a +a+5 -a +a+5>0, a -a-5<0 (a+)(a-5)<0 -<a<5 -a +a+5=-(a-) +9 a=, {, }, (, ) ;!;" (5- ) +( -)Ω ='5 (-) +(-) = {, }, (, 0) ;!;" (+ ) +( - -)Ω =' (-) + =8 +(-b) =r (-, ), (, ) (-) +(-b) =r b -b+5=r +(-b) =r b -8b+5=r, b=5, r =0 (0, 5) r =0 +(-5) =0 (-a) + =r (0, -), (, ) a +6=r (-a) +9=r a -a+0=r, a=-, r =5

143 6 ~ 66 (-, 0) r =5 (+) + =5 (-) + =8 +(-5) =0 (+) + = A+B+C=0 (, ), (, -), (-, 0) 9+6+A+B+C=0 ++A-B+C=0 9-A+C=0 A=0, B=-, C= =0, +(-) = (0, ), ' a=0, b=, r=' a+b+r=+' +' 6 + +A+B+C=0 ABC A, B, C ++A+B+C=0 ++A+B+C=0 9++A+B+C=0 A=-5, B=-5, C= =0, {-;%;}+{-;%;}=;%; æ;%; ;%;p ;%;p 6 =+ (a, a+) (-a) +(-a-) =(a+) (-, -) (--a) +(--a-) =(a+) (a+) =0 a=- (+) +(+) = =0 (+) +(-) =5 (-, ) (+) +(-) = p 65 (a, b) (-a) +(-b) =b (, ) (-a) +(-b) =b a -a-b+=0 (, ) (-a) +(-b) =b a -a-b+8=0 _- a -=0 a= a=b=, a=-b=5 +5= a+b=0(-, ) a+b=0-6a+b=- + --a+b=0 (-) +(-a) =+a -b,, a =" + aç ç- b a =+a -b b= a= a+b= k =0 (+) +(+) =k -5, - =" k - 5 k -5= k= ( k>0) 68 (, ) (-) +(-) = = =0 a=-, b=-6, c=9 a+b+c=- -

144 RPM 0% 0% a, b, c 0% a+b+c 0% k+0=0 (-) +(+k) =k -, =" k - k -=9 k= ' 0 k=' 0 7 (, ) (-) +(-) = (, a) +(a-) = (a-) =0 a= a+0-b=0 (-) +(+a) =a +b-6,, = -a =" a + b-6 a=, b=6 ( a>0, b>0) a+b= a-+b=0(, -) 9++6a++b=0 6a+b=- + +a-+b=0 (+a) +(-) =+a -b,, -a =" + a - b a =+a -b b= a=- b-a= = + -=0 (-) +(-) = + --+=0 ( + -)+k( + --+)=0 (, k+-) (, ) (+-)+k(+--+)=0 -k=0 k= k= ( + -)+( + --+)=0 + --=0 A=-, B=-, C=0 A+B+C=- 7 (, ), r (r, r) (-r) +(-r) =r (, ) (-r) +(-r) =r, r -6r+5=0 (r-)(r-5)=0 r= r=5 (, ), (5, 5) " (5- ) +(5 -)Ω =' 7 r, (r, -r) (r, -r) --=0 r+r-=0 r= p 76 ( + -+-)+k( + ++-)=0 (, k+-) (0, 0) --k=0 k=- k=- ( + -+-)-( + ++-)= =0 77 ( + -6+)+k( )=0 (, k+-) (, 0) (-6+)+k(-+)=0 -+k=0 k= k= ( + -6+)+( )=0

145 66 ~ =0 (-) +(-) =5 '5 p ('5) =5p 5p (-, ) -(a-)+-a+=0 a=8 a= 78 ( + -6+)+k( + +a-+)=0 (, k+-) (0, 0) +k=0 k=- k=- ( + -6+)-( + +a-+)=0 + +a-=0 (+a) +(-) =a + " a +Ω 0p p (" a +) =0p a +=0, a =9 a= ( a>0) 79 (-) + = =0 ( + --6)-( + +-5)=0 ++=0 =-- a=-, b=- a+b=-5 80 ( + -8)-( )=0 -+=0 =;!;+;#; =a+6 ;!;_a=- a=- 8 ( + +)-( + -+)=0 -=0 = (, ) -=(-) =- =- 8 ( + +a+-a)-( + +--)=0 (a-)+-a+=0, + +--=0 (+) +(-) =, + +a+-a= =0 8 + =9, + +++=0, ', A, B, ' AB C + -9-( + +++)=0 ++0=0 + =9 (0, 0) 0 C = =;; 5º;;= " + Ω AC A =, C = AC =øπaπ -πc ='ƒ9-='5 AB =AC ='5 '5 8 AB AB ( + -)-{(-) +(-) -}=0 +-=0, (0, 0) (, ) =, =;!;, =;!; AB ;!; ;!; 85 + =5 + -5=0 (+) +(+) = + +++=0 ( + -5)-( + +++)=0 ++=0 + =5 (0, 0) " + Ω = '5 + =5 '5 æ ('5) -{ } 8 =æ5-9 = '5 5 '5 p { } 6 6 = p p '5 5 5 A B C ' 5

146 RPM =0 (+) +(-) =9, ( + +--)-( k)=0 +--k= =0 (-, ) -+6--k " + Ω = '5 -k æ -{ } k ='5, 9- =5 5 5 k =00 k=0 ( k>0) 87 =m+ + -=0 +(m+) -=0 (+m ) +(m-)+=0 D D =(m-) -(+m )>0 m -m+--m >0, -m>0 m<0 88 (0, 0) m-+-m=0 -m " m + -m <, -m <" m + " m + -m+m <m + m -m<0, m(m-)<0 0<m<;$; -k 5 89 =+k + =5 +(+k) =5 5 +k+k -5=0 0<m<;$; D D =(k) -5(k -5)>0 5-k >0-5<k<5 k M=, m=- M-m=8 =+k + =5 0% k 0%, 0% M-m 0% 8 90 (, ) ++=0 +8+ =: 5 : " + Ω 'a 'a>: 5 : a>: 5ª:=6.76 a 7 9 =m-5 + =9 +(m-5) =9 (+m ) -0m+6=0 D D =(-5m) -6(+m )=0 9m -6=0 m=;$; ( m>0) 9 (, -) ++k=0 6-6+k " + Ω = ' k ' =', k = k= ( k>0) 9 5p '5 (-, ) -+k=0 --6+k " +( -)Ω k ' = -8+k '5 '5-8+k ='5, -8+k =5 '5-8+k= 5 k= k= k +=6 6 9 (, ) 6

147 68 ~ 70 (, ) -+k=0 -+k " + (- )Ω = -+k =, k- ='5 '5 k= '5 k (+'5 )+(-'5 )= 95 =-+ + =k +(-+) =k -+-k=0 D D =(-) -(-k)<0 -+k<0 k<;!; k>0 k 0<k<;!; 96 =-m+ + = +(-m+) = (+m ) -m+=0 D D =(-m) -(+m )<0 m -<0 -'<m<' 97 (a, 0) +=, +-=0 a- " + = a- ' a- ' -+k '5 >, a- >' (a-) >, a -6a+7>0 a<-' a>+' a (-a+) >6, a -a-6>0 (a-9)(a+7)>0 a<-7 a>9 a A, B, (0, 0) -+k=0 H A =, AH =;!; AB =' H =øπa π-πah =" - ( ') = -+k=0 k " + ( -)Ω =, k =' k>0 k=' =0 =0 +0+9=0, (+)(+9)=0 =- =-9 (0, -), (0, -9) =0 (-) +(-) = A, B, C(, ) -+=0 H -+ CH = = " + (- )Ω ' CAH CA = AH =øπca π -πch =æ - { } =æ;&;= ' AB =AH =' 'å - - A H H A - -+k=0 B -+=0 B C 98 p ' (0, a) -+=0 -a+ " + (- )Ω = -a+ ' ' -a+ >', -a+ >8 ' 0 A, B, -+5=0 H 5 H = = " + (- )Ω - B -+5=0 H - A 7

148 RPM AH A = AH =øπa π -πh =" - Ω =' A, B AB p (') =8p 8p -+=0 -+ " + (- )Ω = ' S ' ;!; ' { +' }=0 5 A ' ;;::; =+ B C ' P =0 (+) +(-) =8 (-, ) --= ' = " + (- )Ω, ' 5' 9' 5' a= +'=, b= -'= a+b=5' 0 (, -) -+=0 ++ =' " + (- )Ω, ' '-'=' 05 (0, 0) -+k=0 k " + (- )Ω = k 5, k +=5, k =5 5 k=5 ( k>0) 5 0% k 60% 06 A(0, ), B(, 5) -= 5- (-0) =+ -0 AB =" (- 0) +(5 -)Ω =', =0 (-) +(-) = (-) +(-) = C(, ) ' =0 (-) +(-) = (, ) " + Ω =5 M=5+', m=5-' 5+'-(5-')=' 08 (, ) (0, 0) " + Ω ='5, r (, ) '5+r '5+r=+'5 r= 09 P(a, b)(, ) (, ) P d-r d r (0, 0)(, ) d d=" + =5, r= " (a- ) +( b- )Ω 5-= =0 (-) +(+) = (-, 0), (, -) -0= --0 (+) = (, )(-) +(+) =0 (-)(-)+(+)(+)=0 +-0=0 a=, b=-0 a+b=-7-7 8

149 70 ~ 7 + =5 (, ) +=5 +-5= =0 (+) +(-) =0 (+) +(-) =0 (-5, ) (-5+)(+)+(-)(-)=0 -+7=0 +-5=0 -+7=0,, =0 =-5, = -5++(-5+)-(+)-5=0 -+7= =0 (-) +(+) =8, (-) +(+) =8 (5, ) + (5-)(-)+(+)(+)=8 +=6 ;!;_6_6=8 8 + =5 (-, ) -+=5 =;!;+;%; (a, b) a+b=5 =-;ba;+;b%;, ;!;=-;ba;, ;%;+;b%; b=-a, b+, (a, b) + =5 a +b =5 a +a =5, a = a= a=, b=- ( b+) a+b=- 5 +'=8, =- +' ' {5,} 6 - ' ' + =9 =' " (' ) +Ω =' 9 9, -9 PQ = =0 (-) +(+) = 5 tan5 = (-) +(+) = += (-) '" + +=- =- =-6 =- =-6 =+b, -+b=0 (, -) ' ++b " +( -) Ω =', +b = +b= b=- b=-6 --=0 --6=0 7 =+b (, -) -+b=0, ++b " + (- )Ω b=- '5 =, +b ='5 b (-+'5 )_(--'5 )=- 8 m '5 =m '5" m + 5 "5 (m +)=5 5(m +)=5, m +=5 m = m= 9

150 RPM _(-)=- - 9 (, ) m -=m(-) m--m+=0 (-, ), -m--m+ " m + (- )Ω -m =" m + = -6m+9m =m +, 8m -6m=0 m(m-)=0 m=0 m=;#; ;#; 0 C, P, Q APCQ CAP CA =CP +AP (-) +(5+) =r +r, r =0 r =0 r='5 ( r>0) C(, -) r P Q A(, 5) CPQ ('5) = +PQ, PQ =6 PQ = ( PQ >0), CPQ=;!; CQ PQ =;!; CP QM ;!; =;!; '5 QM QM = QR =QM = + -+-=0 (-) +(+) =9 C(, -)A(-, ) CA ="( - -) +( + ) Ω CA ='å ABC AB =" (' ) - =5 (0, 0) A(5, 0) 5, AP AP =" 5 - (' 0 ) =' 5 8'5 5 '5 5 A(-, ) ' 0 B ' P 5 C(, -) A(5, 0) A(0, a) m =m+a (0, ) m-+a=0 -+a =, a- =" m + " m + (- )Ω 9m -(a -a-5)=0 m, m -(a -a-5) m m = =- 9 a -a-=0 a 5 P =, A = AP AP =" - Ω =' APB _ AP=_{;!;_'_} =' 6 P, C(, -) AP +CP =AC +(' 0 ) =(-a) +(--0) a -a-=0, (a-7)(a+)=0 a=7 a=- a 7+(-)= P(, ) Q, R + +-+=0 (+) +(-) = C(-, ) CQ =, CP =" (+ ) +( -)Ω ='5 C Q M R P(, ) 7 + =0 (, ) +=0 =-;!;+: º: + =0 50

151 7 ~ 7 = ' 0" + = 0 =+0 =-0, {-: º:, 0}, (0, 0) {: º:, 0}, (0, -0) ;!;_: º:_0=;:@);º: (-) +{+;A;}= a +7 a +7=6, a =6 a= 6 (, ) (, -) " + Ω =' 8 + = (, ) += (-, ) -+= A{: :, 0} B{-: :, 0}, P(-, 5) PAB ;!;_{: :+: :}_5=: : 9 PA PB = PA =PB, PA =9PB {(+) + }=9{(-) + } + -0-=0 0 AP BP = AP =BP AP =9BP P (, ) (+) + =9{(-) + } + -5+=0 {-;%;}+ =;(; : : P {;%;, 0}, ;#; P H PAB=;!;_AB _PH AB = PH ;#; PAB ;!; ;#;= + -+a-=0 A B - H P + +(m-)-m+m -=0 (+m-) +(-m) =(m-) +m -m + (+m-) +(-m) =-m-m -m-m >0, m +m-<0 (m+)(m-)<0 -<m< m -, -, 0 (-) +(+) = (-) +(+) = C(a, b) a= -+7 =, b= -+ =0 C(, 0), AC AC =" (7- ) + =5 (-) + =5 (-) +(+) =9 (-) +(+) =0 (, -) (-)(-)+(-+)(+)=0 (-)+(+)=0 += 5 (a, a+), r (-a) +(-a-) =r (, 6) (-a) +(5-a) =r a -a+6=r (-, ) (--a) +(-a) =r a +a+0=r, a=, r =6 C B(-, -) A(7, ) 5

152 RPM, (-) +(-) =6 a=, b= a+b= 6 +'= - ' ' ' + = =' 'å" (')Ω ç+ =' ' 7 =+k -+ -+=0 -(-k)+k -k+=0 D D =(-k) -(k -k+)>0 k -k-7<0 -'<k<+' k -, 0,,, 5 8 P (, ) PA +PB =0 (+) + +(-) + =0 + = 9 + -a-6a+0a-0=0 (-a) +(-a) =0a -0a+0, 0a -0a+0,, 0a -0a+0=0(a-) +0 a=0 S a=0p ' '--k = " (' ) Ω +Ω -k =6, -k= 6 k=-5 k=7 k>0 k= =0 (-) +(-) = C(, ), ' PC ="( - ) + ( -5)Ω =' CT =' PT =øπpc π-πct PT =" (' ) -( ') PT = =+k + =9 +(+k) =9 5 +k+k -9=0 D D =(k) -5(k -9)=-k +5 D>0, -k +5>0, k -5<0 -'5<k<'5 -'5<k<'5, D=0, -k +5=0, k -5=0 k= '5 k= '5, D<0, -k +5<0, k -5>0 k<-'5 k>'5 k<-'5 k>'5, T ' C(, ) P(, 5) 0 (0, 0)A(6, 8) " 6 + 8Ω =0 M m M=5+0=5, m=0-5=5 M-m=0 A(6, 8) (, -), (-r) +(+r) =r (, r>0) (, -) (-r) +(-+r) =r r -6r+5=0, (r-)(r-5)=0 r= r=5 (, -), (5, -5) " (5- ) +( -5 +)Ω =' '+-k=0(-') +(+) =9 (', -) '+-k=0, 5 P(a, b), AP M(, ) 5

153 7 ~ 76 = -+a, = a=+, b=- P(a, b) + -+=0 a +b -a+b=0 (+) +(-) -(+)+(-)=0 + --= k+9=0 (+) +(-k) =k -5 k<0 +b " k -Ω5= -, k -5= k =9 k=- k= k<0 k=- + --=0 7 ( )+k( )=0 (, k+-) (-, -) k(+++8-6)=0 -+k=0 k= k= ( )= =0 (+) +(-5) =6 (-, 5), =a+ 5=-a+ a=- 8 P (, ) PA =PB PA =PB (-) + =(+) +(-) 6-+=0 P PA =PB PA =PB {(-) + }=(+) +(-) =0 (-) +{+;@;}=: 9 : P PA +PB =9 (-) + +(+) +(-) =9 -+ -=0 {-;!;}+(-) =;%; P P, 9 A(, ) P (+) +(-) =r r P, Q C(-, ) CQAP CAP CA =CP +AP (+) +(-) =r +r, r =0 r=' 0 ( r>0) 50 (0, 0) =+k H AB =8 AH =, (0, 0) -+k=0 H k k H = = " + (- )Ω '5 AH A =H +AH k 5 ={ }+, k =5 '5 k='5 k>0 5 (+) +(-) --( + -)=0 -+5=0 (-, ), (0, 0) =-, =-, = {-, } 5 (-a) + --{ +(-b) -6}=0 -a+b+a -b +=0 A 5 H =+k B (0, 0) A(, ) Q {-, } 5

154 RPM b a -b =0 a a --=0 b a -b + - =-, - =- a a a=, b= ab= 5 (, ), (-, ), (, 5) + +a+b+c=0 a+b+c=- -a+b+c=- a+5b+c=- - a=0 - -a-b=, b=-8 a=0, b=-8, c= =0 +(-) =0 (, ), (-, ), (, 5) 0p 0p 0% a, b, c 0% 0% =0 (-) +(+) = (, -) ++=0 -+ =' " + Ω M m M='+, m='- 0Mm=0('+)('-)=0 0 0% 0% M, m 0% 0Mm 0% 55 = (t, t), r +-=0, +-7=0 r t+t- t+t-7 r= = " + Ω " + Ω 5t-= (5t-7) 5t-+5t-7 '5 5t-=-5t+7 t=, r= 5 '5 (, ), 5 (-) +(-) =;5$; =0 (+) + =5 + -a+-6=0 (-) +(-) =;5$; 0% 0% 0% (-a) +(+) =a +7 (-, 0) ( + +-)-( + -a+-6)=0 (a+)-+=0 (a+)-+=0 (-, 0) -(a+)+=0 a=0 0 5

155 76 ~ 77 0% 50% a 0% 57 PQ (, 0), (-) +(-) =6 PQ + =6, (-) +(-) =6 PQ + -6-{(-) +(-) -6}=0 +-5=0 58 lt(, -) T l T -;$; l ;#;, (a, b) ;ab; l ;ab;=( l)=;#; 59 P (, ) AP BP =, AP =BP, AP =9BP (+) + =9{(-) + }, + -=0 {-;#;} + ={;#;} P H PAB=;!;AB PH AB = PH ;#; PAB ;!; ;#;= - P (-) +(-) =6 - T(, -) A B - H Q P{,} l P(a, b)(-) + = C(, 0)A(-, 0) ACP n ;!; b =n(, n, b ) b =;N; n=,,, b P n=, P ACP P _+= 6 =;!; + = +{;!;} =, ;%; = = A, B '5 '5 '5 '5 A{-, - }, B{, } AP +BP '5 '5 '5 '5 =[{+ }+{+ }]+[{- }+{- }] =( + )+8=0 + =, P (, 0), (-, 0), (0, ), (0, -) 6,, A C - '5 5 ( ) P 0t 0t ( ) C(50, -00), t P, C(50, -00) Q P(0t, 0), Q(50, 0t-00) PQ 00 " (50-0t) +( 0t- 00)Ω 00 (50-0t) +(0t-00) 0000 t -t+5 0, (t-5)(t-9) 0 5 t Q P(a, b) =0 (-) + = 55

156 RPM 6 (-+, 0-), (0, -) (+, -), (, ) (+, --), (, -) (-+, -5-), (-, -6) (0, -) (, ) (, -) (-, -6) 6 (0, 0) (0+, 0-) (, -) (-, 5) (-+, 5-) (, ) (6, -) (6+, --) (8, -5) (0, 7) (0+, 7-) (, ) (, -) (, ) (8, -5) (, ) 65 (-, ) (, ) (+a, +b) (, -) -+a=, +b=- a=, b=- 66 -=(+)+ =+5 (+) +(-) -(+)-(-)+= =0 a=, b=- = =0 67 +=-(-)- =- {(-)+} +{(+)-} = + = =- + = 68 =- (, ) (+a, -a) +a=(-a)- =-a- =-5 -a-=-5 a=;!; ;!; 69 (-, -) (, ) (, -) (, -) (-, ) 70 -(-)+=0 ++=0 (-)-+=0 +-=0 (-)-(-)+=0 --=0 = -+=0 --=0 7 (-) +(--) = (-) +(+) = (--) +(-) = (+) +(-) = (--) +(--) = (+) +(+) = = (-) +(-) = (-) +(-) = 7 -=(-) - =-(-) + =(--) - =(+) - -=(--) - =-(+) + = =(-) - 7 (, ) -+ =0, + =0 =, =- (, -) -+ =, + =- =7, =- (7, -) -+ =a, + =b =a+, =b- (a+, b-) (, -) (7, -) (a+, b-) 7 -+=0 (a, b)(, ) (, ) a+ =, b+ = a=-, b=- (a, b) -+=0 a-b+=0 (-)-(-)+=0 --=0 75 { +a, -+b } --=0 A, B -+=0 AB - AB -+=0 +a -+b - +=0 a-b+6=0, AB - b+ a- =- a+b-=0, a=-, b= B(-, ) 56

157 79 ~ 8 76 (, -) (, ) (+a, +) (+a, -+), (a+, -) =- -=(a+)- a=- 77 (, -) (, ) (+a, -) (+a, --), (a+, -) a+=, -=b a=-, b=- a+b= A(, ), B(, -), C(, 5) ABC ++ +(-)+5 {, }, (, ) (, ) a, b (, -) +a=, +b=- a=-, b=- ab= ABC 0% a, b 50% ab 0% 79 (-, ) (, ) (, ) (5, ) (5, 5) (7, 5) (7, 6) P 6 (7, 6) p=7, q=6 p-q= 80 =a+b -, -=a(+)+b =a+a+b+ =+ -, a+b+=, a_=- a=-;!;, b=-;!; a-b=0 8 +-=0 -, ;!; (+)+{-;!;}-=0 ++=0 ++=0 a+b+=0 a=, b= a+b=6 6 8 (, ) (, ) (+a, +b) (, ) +a=, +b= a=, b= -+=0, (-)-(-)+=0 -+7=0 (, c) -c+7=0 c=8 a+b+c= 8 =- m, - -(-)=(-m)- --m-7=0 --=0 '5 --=0 (0, -) -m-7 ='5 " + (- )Ω m+ =0', m+= 0' -+0' m= ( m ) -+0' 0% 0% m 0% =0 (+) +(+) =9 ' =0 (-) + =9 (-, -), (, 0) (-, -) (, ) (+a, +b) (, 0) -+a=, -+b=0 a=6, b= a+b=7 7 57

158 RPM =0 (+) +(-) =5 (-, ) '5 (+) +(-) =5 '5 -, - (+) +(-) = =0 (+) +(+) =5 '5, -=(-k)+ =-k+ = -5- -k+= k-5=0 D D =6-(k-5)=0 -k+6=0 k= 90 + = a (a, 0) ++=0 (a, 0) a+ =, a+ =5 " + Ω a+= 5 a=;#; ( a>0) 86 = +6+a=(+) +a-9 (-, a-9), = (0, 0) (, ) (+, -a+9) +-=0 (-)+(+a-9)-=0 ++a-=0 ++a=0 a=a- a= 87 + =6, - (-) +(+) =6 =0 (-) +9=6, (-) =7, -= '7 =+'7 =-'7 (+'7)-(-'7)='7 88 =- a, a -a=(-a)- =-a- (, -) -=-a- a= 89 =+ k, + = b (0, b) ++=0 (0, b) b+ =, b+ =5 " + Ω b+= 5 b= ( b>0) a=;#;, b= 9 (-) +(+) = a, b (--a) +(+-b) = (, -), (+a, -+b) " a + bω = a +b =6 9 P(, ) Q(-, -) R(, -) PQR=;!; QR PR =;!; = Q(-, -) a +b =6 0% a, b 60% P(, ) R(, -) 58

159 8 ~ 8 9 A(, -) B(, ), C(-, -) BC +(-) +(-) {, }, (0, 0) (0, 0) 9 A(-, ) B(, -) AB ="( + ) + (- -)Ω ='å0å0=0 0 =-n n= m+n= a-6+=0 (-a) +(-) =a +5 (a, ) (-a, ) =-;!;+;!; =-;!; (-a)+;!;, ;A;=;%; a= P(-, -) (-, ) (, -) (-, -), P 00=_+ 99 (-, -) 00 (-, ) -=--= =0 (-)-+5=0 +-5=0 -;$; -;$; (, ) -=-;$;(-) +-=0 a=, b=- a+b=-8 97 =a+ -=a+ -a--=0 -+b=0 a=-, b=- a+b= (+) +(-) = (-+) +(--) = (-) +(+) = a+b=0 + +6a-b=0 (+a) +(-b) =9a +b (-a, b), = ++0=(+) + (-, ) -a=-, b= a=, b= ab= 0% 0% ab 0% 98 =;!;+ =-;!;+ (-6, ) -=(+6) =+0 99 =m+n -=-m+n =m-n =+ m=, =-n(, ) 0 (, -) k (-) +(+) =k (-) +(-+) =k (-) +(-) =k (, -) (-) +(--) =k k=5 ( k>0) 0 =+a =-+a 59

160 RPM + --+=0 (-) +(-) = (, ) (, ) =-+a a= 05 ++a=0 --+a=0 +-a=0 (-) +(+) =9 (, -), --a =, 9-a =5 " + Ω 9-a= 5 a= ( a>0) =0 (-) +(-) +(-)-(-)=0 + -+=0 (-) +(+) =5 (, -), '5 =+k, -+k=0 ( )<() -(-)+k <'5 " +( -)Ω k+ <'å0 --'å0<k<-+'å0 --'å0<k<-+'å0 0% 0% k 0% 07 l =+a -=-+a m =-a l, m l (0, a) m --a=0 'å0, -a-a ='å0 " +( -) Ω a =0, a= 0 a=-5 a=5 a -5 5= =0 (-) +(+) =9 (, -) (, -)(, ) (a, b) +a =, -+b = a=, b=5 (, 5) (-) +(-5) =9 (, -)(, ) ( -, -(-)), (, 5) (, 5) (-) +(-5) = 09 A(, ), C(, -5) AC B(, ) + =, -5 = =0, = -= (, -5)=( -, -) =(-, 6-) -=, 6-=-5 =0, = -= 0 +-=0 (, 0)(-, ) (a, b) +a =-, ;B;= a=-5, b= - (-5, ), -=-(+5) ++= =0 (+) +(+) = (-, -), (-, -)(-, ) (a, b) -+a =-, -+b = a=-, b= 60

161 8 ~ 85 (-, ), (+) +(-) = =0 ++= =0 (, )(-, ) (', ') +' =-, +' = =--', =-' +-=0 --'+-'-=0 ++=0 P P P = -+=(-) + (, ) =- +6-5=-(-) + (, ) P{ +, + }, P(, ) = = (a, ), (b-, ) a=, b-= b= a+b=5 P(, -) = Q(-, ), P(, -) R(, ) PQR +(-)+ -++ {, }, {, ;@;} {, ;@;} +-=0 = +-=0 -;@;-+=0 a+b+=0 a=-;@;, b=- ab=;@; 5 (-) +(+) = (, -) = (-, ) (-, ) (, ) (, ) (, ) =a+ =a+ a=0 0 = 0% 0% a 0% =0 (+) +(-) =5 =- -, - (-+) +(--) =5 (+) +(-) =5 =+k (-, ) =+k, =-+k k= =0 =- ---=0, ++=0 =-;!;-;#; a=-;!;, b=-;#; a+b= a+b-8=0 {+;A;} +{+;B;} = a +b +8 {-;A;, -;B;} =- {;B;, ;A;} (-, ) ;B;=-, ;A;= a=, b=- a-b=8 8 9 =- =- -=-- =;!;-;!; - (, ) - 6

162 RPM -=-(-) = a++c=0 (+a) +(+) =a -c+ + +b-6=0 (+b) +(-) =b +9 (-a, -), (-b, ) =+ (-a, -), (-b, ) -a-b -+ {, } =+ = -a-b + a+b=0, (-a, -), (-b, ) =+ + _=- -b+a 8=b-a a -c+=b +9,, a=-, b=, c=-8 a-b-c=0 (, -) -+=0 (a, b) { +a, -+b } -+=0 +a - -+b +=0 a-b+6=0, (, -), (a, b) -+=0, =+ b+ _=- a- a+b=, a=-, b= (, -) -+=0 (-, ) - --=- + += (, -) -+=0 (-, ) (, 0) (a, b) { +a, b } -+=0 +a - b +=0 a-b=-, (, 0) (a, b) -+=0 b _=- a- a+b=, a=-, b= a+b=- (0, 0), (, -) (, -) a+b+5=0 a-b+5=0, (0, 0), (, -) a+b+5=0 - {-;ba;}=- b=-a, a=-, b= a+b= 0% 0% a+b 0% (-a) +(-) =, - (--a) +(+-) = (--a) +(+) = = (--a) +(+) = (-, +a) ()= ( ), +a =, a+= a=- a=0 5 P(a, b)p, (a+, b+) (a+, -b-) a+=-, -b-= a=-, b=- P(-, -) P(-, -) 6

163 85 ~ 87 6 (+) +(+) =6 - (+) +(+) =6 =- (-+) +(-+) =6 (-) +(-) =6 =0 (-) +9=6 (-) =7, -= '7 =+'7 =-'7 PQ =(+'7)-(-'7) ='7 7 =+ a -a=+ =++a -=-++a =--a + -++=0, (-) +(+) = (, -) -=--a a= 0% 0% a 0% AP +PQ +QB =A'P +PQ +QB' æa'b' ="( + ) + (- -)Ω =7' 0 A, B A(0, 0), B(60, 0) A A'(0, -0) B =50 B'(60, 60) P, Q AP +PQ +QB =A'P +PQ +QB' æa'b' A'(-, ) ="( 60-0) +(6 0+ç0) Ω =' 00ß0å0=00(m) 50 A' A 0 P P 60 A(, ) B(, ) Q B'(, -) 00 m 0% A, B 0% B' 0 B 0% Q 8 A(, ) = A' A'(, ) AP +BP =A'P +BP 9 B = æa'b A P ="( 5- ) + (9 -) Ω ='7å 9 A(, ) A'(-, ) B(, ) B'(, -) A' 5 f(, )=0 f(-, )=0, = f(-, )=0 f(, )=0 - k f(-, )=0 f(-, )=0 = (-, 0) (0, 0) (0, 0) = (0, ) (, ) (, ) k f(-, )=0 6

164 RPM = (, 0) (, 0) (0, ) f(, )=0 f(, )=0 = f(, )=0 f(-, )=0, f(-, -)=0 - - f(-, -)=0 f(, )=0 - f(+, )=0, = f(+, )=0 - f(, )=0 k f(+, )=0 5 f(, )=0 f(, -)=0, - f(+, -)=0 g(, )=f(+, -) 6 (, ) (+a, +) (, )(, b) +a=, +=b a=, b=5 a+b=6 7 (, ) (-, ) (+) +(-) =r (-, ) (-+) +(-) =r, r = r=' ( r>0) f(+, -)= f(+, )=0 k f(, )=0 f(, -)= f(+, )= =0 (-) + = + --+=0 (-) +(-) = + +-+=0 (+) +(-) =, 9 (, -6)(a, b) (, ) (a, b) (, -6), (, ), + =a, -6+ =b a=, b=- a+b= =0 (+) +(-) =9 (-, ) =- (a, b) (-, ), (a, b) a- b+ {, } =- b+ =- b=-5, (-, ) =- a=- (+) +(+5) = =0 (+) +(-) =9 =- (-)-, (+) +(---) =9 (+) +(+5) =9 (, ) (, ) (+c, +d) (-, ) +c=-, +d= c=-, d= -+=0 -, (+)-(-)+=0 -+9=0 +a+b=0 a=-, b=9 a+b=5 6

165 87 ~ 89 + = = + = = =- = =-, =- = - = = - =, - =- = =, (-) +(+) = (, -) (a, b) (+) +(-) =c (-, ) - -+ =a, =b a=-, b=, c= a+b+c= (-) +(+) =(a, b) (a--) +(b-+) = (-a+) +(-b-) = (+) +(-) =c -a+=, -b-=-, c= a=-, b=, c= a+b+c= = +-5 (, ) (+a, +b) -b=(-a) +(-a)-5 --b=(-a) +(-a)-5 =- +(a-)-a +a+5-b =- a-=0, -a +a+5-b=0 a=, b=9 a+b= 5 (, ) --=0 (a, b) { +a, +b } --=0 +a - +b -=0 a-b-=0, (, ), (a, b) --=0, =;!;- b- ;!;=- a- a+b-6=0, a=5, b=- (, ) --=0 (5, -) 6 =a+b (, ) (, -) +=a+b =a+b- -+6=0, =;!;+ a_;!;=- a=-, -+6=0 =b- b= ab=- 7 = ++=(+) + =- +6-=-(-) - (-, ), (, -), (a, b) -+ - {, }=(a, b) a=, b=- ab=- 8 =+k -=(-)+k --k=0 + =0 (0, 0), -k ='å0, k =5' " +( -) Ω k=5' ( k>0) 9 (-, 5) (, -5),, - (+, -5-), (5, -7) = (-7, 5) a=-7, b=5 a+b=- 50 (-) +(-a) = -, (+-) +(--a) = (+) +(--a) = = (+) +(--a) = (+a, -) +a =, a+= a=0 a=- a

166 RPM 5 P(, ) =+ Q(a, b) P(, ), Q(a, b) { +a, +b } =+ +b = +a + a-b=-8 P(, ), Q(a, b) =+ b- =- a+b=6 a-, a=-, b=7 Q(-, 7) PQ ="( - -) +( 7- )Ω =5' 55 ;{;+;};= += m, (-m)+(-)= +=m+ m+, m+ m>0 m+ ;::::; ;!; (m+) m+ =6 m+ (m+) =6, m+= 8 m=- m= m>0 m= 5 A(, ) A'(, -) AP +BP =A'P +BP æa'b ="( 6- ) + (+ç) Ω =' 5 + -=0 (-) + = (, 0) a, - (+a, 0-), (a+, -) +-5=0 (a+, -), (a+)+ (-)-5 = " + Ω a-6 =5, a-6= 5 a=;!; a=;; ;; a ;!;+;; ;;= 5 P(, ) (, ) (+, -) (, ) (-, +) 6 (, ) (+-, -6+), (+8, -) =, = Q (9, -) PQ ="( 9- ) + (-ç-ç) Ω=' 7 A(, ) P A'(, -) B(6, ) a+5=0 (+) +{-;A;} =+ =- {-, ;A;} =-, ;A;= a=6 p{+ a }=p{+;; ;;}=p 57 f(, )=0 f(-, )=0 = f(-, )=0 f(, )=0 k a f(-, )=0 f(-, )=0 = (, ) (-, ) (, -) =0 -++=0 --=0 = --=0 -+=0 =- k - - a ;; f(-, )=0 66

167 89 ~ 9 (-a) +(+) = -+=0 (a, -) a++=0 a=- - 0% = 0% a 0% a+b=;(; ;(; 0% 0% 0% a+b 0% 59 +(-) =9 (-) + =9, (0, ) (, 0), - +-=0 -, + -+(+)-=0 +-=0 +a+b=0 a=, b=- a+b=- - (, ) (+, -) 0% +-=0 0% a+b 0% =0 (-) +(-) = (, ) =0 (-) +(-6) = (, 6) (, ), (, 6) { + +6, }, (, ) =a+b =a+b (, ), (, 6) =a+b 6- - a=- a=-;!; a=-;!; b=5 6 -+=0 P(, ) Q{','} +-=0 Q(', ') PQ P{,} -+=0 +-=0 +' +' {, } +-=0 +' +' + -=0 +'++'=, PQ +-=0 -' (-)=- -' -'=-', =-', =-' (, ) -+=0 -'-(-')+=0 '-'=0 ', ', -=0 -=0 0% 0% 0% 6 A -6+=0 A'(a, b) A'{a,b} A(, -), A'(a, b) A{,-} { a+ b-, } -6+=0-6+=0 P B{,} 67

168 RPM a+ -6 b- +=0 a-b=-8 A(, -), A'(a, b) -6+=0 b+ =- a- a+b=, a=-, b= A'(-, ) AP +PB =A'P +PB æa'b ="( + ) +( -)Ω = 6 f(-, -)=0 5, - f(-(-5), -(+))=0 f(-+5, --)= f(, )=0 f(, -)=0, f(-, -(-))=0, f(-, -+)=0 f{,}=0 f{-,+}=0 f(-, -+)=0 -, - f{,-}=0 + = f(, )=0 f(-, )=0 f(-, -)=0 = f(-, -)=0 f(-, -)=0, (-, ) "( -) + +='5+ "( -) + -=' P, Q, R, R A, B R', R" BR=a, RA=b PR =PR", QR =QR' R"B= BR=a R'A= RA=b PQ +QR +RP =PQ +QR' +PR" ær'r" '5+, '5- AB=5 R"R' R'R" =øπr' π +πr"μ =" + Ω=' ' P R'' a a b b Q B R' R A 65 A A' A'(-, ) B B' B'(, -) AP +PQ +QB =A'P +PQ +QB' æa'b' B(, ) A'(-, ) A(, ) P ="( + ) + (- -) Ω ='8å5 Q B'(, -) '8å5 68

169 9 ~ 9 68 =-( ) >0 <;!;+ =;!;+ ( ) 70 = +-8 ( ) 7 (0, 0) ( ) 7 (, -) ( ) (-) +(+) 9 (, -) ( ) = = = - - =- -8 (-) +(+) =9 - (-) +(+) =9 7 =- ( ) =-+( ) 75 =+ ( ) =-( ) 76 (0, 0) ( ) =+( ) 77 (-) +(+) <5 [ (+) +(-) >7 (, -) '5 ( ) (-, ) '7 ( ) (+) +(-) = =-+, =+ =-+( ) =+ ( ) >-+ [ <+ 79 =- +9 =;!;- (-) +(+) =5 ( ) = = =- =- =+ - + = 69

170 RPM ( ) - +9 æ;!;- 80 +=0 =- -+=0 =;!;+;#; = + (-, 0) - (-, 0) =- ( ) 8 +-=0 =-+ --=0 =- (, 0) (, 0) ( ) 8 =0, =0, --=0 = - (, -) (, -) ( ) 8 -+=0, +-=0 (, ) (-+)(+-) =, = (-+)(+-)>0 (-+)(+-)æ0 - =- =-+ = - 85 (+) +(+) =8 =0 =0 (-, -) ( ) =-, =- (-)(-)(+---6)<0 ( ) 0 86 =- + = (, 0) (-)( +-) =, =0 (-0)(+0-)>0 (-)( +-)>0 87 -, ( ) 88 =+k =, = =+k k= =k(k ) =-+k k - k (, ), (-, ) k, -, - 90 = -6+5 > -6+5 (k, -) - ->k -6k+5, k -6k+8<0 (k-)(k-)<0 <k< a=, b= a+b=6 6 8 =, + = (, 0) (-)( + -) =, =0 (-0)(+0-)<0 (-)( + -)<0 9 +_-(-)+=>0 (-) +_(-)-+=>0 +_-+=5>0 0 +_0-+=>0 (-) +_(-)-+=-<0 70

171 9 ~ 95 9 =- + ( ) (-) +(-) =5 ( ) p 5 =5p 5p 9 (a, ) =-- >-a- a>- (, a) =+ a<+ a<, -<a< a -, -, 0, (a, ) =-- a 0% (, a) =+ a 0% a 0% = <0 (a, ) a +9-a-+<0 a -a<0, a(a-)<0 0<a< (-) + (-) + (-) + = ( ) 98 (-, ), (, -) ++k=0 (-++k)(-6+k)<0 (k+)(k-)<0 -<k< 99 (-, ), (0, ) ++k=0 (-6+6+k)(0++k)<0 k(k+)<0 -<k<0 k -, =- --=0 A(, k), B(k, ) AB (-k-)(k--) 0 (-k)(k-) 0 (k-)(k-)æ0 k kæ k kæ 50 =m+m m-+m=0 A(, 0), B(, ) AB (m+m)(m-+m) 0 m(m-) 0, m(m-) 0 0 m a=0, b= a +b = 96 (a, ) + =5 ( ) a +>5 (a, ) + =9 ( ) a +<9 5<a +<9, <a <5 <a<'5 ( a>0) (-) +(-) 5 (-) +(-) =9 ( ), æ-+ =-+( ) 50 +< æ- [, [ +<- +5 <- + æ- =- ( ), <- + =- + ( ) 7

172 RPM 50 > - = = æ+ =+,, - - =@- =+ = = + æ æ0, æ0, +æ æ0, <0, -æ <0, æ0, -+æ <0, <0, --æ (, 0), (-, 0), (0, ), (0, -) 505 =+, + = (, ) (-+)(+-)>0 (, ) 506 =0, =0, =- + (-, ) - (+-)<0 (-, ) 507 =, =-, + = (, 0) (0-)(0+)(+0-)<0 - - (, 0) 508 =, =+ (, 0) (- )(-+) (0-)(-0+)<0 (, 0) ( ) (- )(-+) =- ( ) + = ( ) - [ + 50 =0, =, (-) +(-) = (, ) (-)( + --+) (-)(+-8-+)<0 (-)( + --+) 0 5 =' ( ) + = ( ) ' [ + > 5 + = ( ) + =6 ( ) =, (, ) = (, 0) 7

173 95 ~ 98 ( + -)(- ) (+0-)(0-)>0 (, 0) ( ) ( + -)(- )æ0 5 =0, =0, =-, =, + = (, ) (+)(-)( + -) (+)(-)(+-)>0 (, ) ( ) (+)(-)( + -)æ0 55 +æ =-+ ( ), + + = ( ) p_ _;!;-;!; =p- = = =-, + k + =k p ;!;_p_k =p k=( k>0) (-) + (0, ), + r r + + r + =r -r r +(-) = r - ræ r -k k k = =6 ( ), (+) + æ (+) + = ( ) + =6 p_ -p_ =p - - (+) + = - 57 æ0, æ =-+, -+æ0 =+ =+ - =-+ {;!; }-{;!; }=;&; ;&; = ( ), æ+k =+k( ) + + = =+k æ+k - + = =+k - +(+k) =, +k+k -=0 D D =k -(k -)=0 -k +=0 k= ' + æ+k k -' k -' 5 æ =, æ-+k =-k+k 7

174 RPM æ æ-+k = =-+k =-+k, +-k=0 D D =+k=0 k=- k k - - =-+k =@ (, ) 8 56 ( ) -=k(k ) =-k (0, )k, =-k k=-, (, 0)k, 0=6-k k=6 M=6, m=- Mm=-8 =-k = = = æ0, æ0, + -+ æ0, <0, - æ- <0, æ0, -+ + <0, <0, -- æ-- ~ + ( ), (, ) -,, (, ) (, ) _+=5 5 '5 + =5 =- ( ) + =5 ( ) -'5 -'5 '5 =- (, ) 5 =0( ), =-+5 ( ), =+ - ( ) (, ) 9-5 =+ 5 = ( ) =-+9 9 =-;;+ +=k(k ) =-+k =-+k+-6=0 +-9=0 (, )k =-+k k= =k(k ) =-;#;+;K; ;K; -;#; (, )k + = ;; 9 (, ) 6 =-+k 0% + 60% 55 = ( ) =+ ( ) = - - = ( ) -=k(k ) =-k - =-k - + = 7

175 98 ~ 00, k (0, 0) --k=0 -k = k= '5 " + (- )Ω - M='5, m=-'5 M +m = ( ) = +k - =k(k ) = +k (, 0), k =- + - m=- =- +,k +k=- + -+k=0 D D =-k=0 k=;!; M=;!;, Mm=- 5 +, ( ) +=k(k ) =- +k + =, k (k-)+ = -+k-=0 D D=(-) -(k-)=0 k=;%; + ;%; ;%; 5 ( ) - =k(k ) = +k =+, k +k=+ -+k-= = - = +k =+ =- =- +k D D=(-) -(k-)=0 k=;%; - ;%; 5 ( ) - =k(k ) = +k (0, ),k -_0= (-, -),k --_=-, - +(-)=- 5 ( ) + =k(k>0) 'ßk +-=0, k 'ßk - ='k, 'ßk=' " + Ω k= ( ) + =k(k>0) = +k 'ßk (, 8),k =+ +8 = =k(k>0) 'k - = =k =;;-;; =-+ = - + =k += 75

176 RPM (, ), k 9+= (, ), k +=, M=, m= M+m=5 57 ( ) (-) +(-) =k(k>0) (-) +(-) =k (, ) 'k += (0, 0),k +=8 +=,k += =-+ (-) +(-) =k (-) +(-) =k, -+-k=0 D D =(-) -(-k)=0 k=, 8+= ( ) ;[};=k (k ) =k k (, ),k ;@;= (, ),k ;#;=, _= =-+ (, ) =k = (, ) = k (-, 0) k (, ), k + =;!; 50 ( ) - =k(k ) - -=k(-) =-+ k(, ) k (, 0),k 0- M= =;$; - (0, ),k - m= =;!; 0-, M-m=;$;-;!;=;6%; 5 A, B kg, kg +(L), +(m ) ( { æ0 æ0 =k(+) +=0 0 +=0 ( 05 (0, 90) ) 70 5+=k(k ) 55 5+=k +=0, +=0 (0, 90),k B 90 kg - 59 =k(k ) + =k(+) 5 A, B kg, kg 0+0(kW), +(m ) 76

177 00 ~ 0 ( { + 90 æ0 { æ0 9 æ0 9 æ0 ( 0 ) 5+8=k(k ) 6 (8, ) += 6 ( ) 5+8=k 0 (0, 0) +=90 +=8 +=k(k ) +=, += (8, ),k 0+0=00 +=k 0+0=00, +=90 (0, 0),k 5_8+8_=6() A 0 kg, B 0 kg A 0 kg, B 0 kg 55 A, B 0 g, 0 g 0.+0.(kcal), (g) 0% 5 A, B, P, Q +(kg), +(kg) ( { 9 60% A, B 0% æ0 æ0 +=k 0 +=0 ( ) (6, 8) =k(k ) +=0 +=0, +=0 (6, 8),k _6+_8=() 5 A, B, +(), +() ( ( { 9 ( 0.+0.=80 +=k = (50, 00) ) 00 +=k(k ) =80, = (50, 00),k a+b = X, Y A B 0+0(mg), 8+(mg) ( { æ æ æ0 æ0 0+0æ0 8+æ0 æ0 æ0 ( ) 0+0=k(k ) 8+=0 0+0=0 5 (, ) 5 ;; 0+0=k 77

178 RPM 0+0=0, 8+=0 (, ),k 0_+0_=0( ) 57 P(-, 5), Q(, -) a-+a=0 (-a-0+a)(a++a)<0 (a-0)(5a+)<0 -;5@;<a<5 58 = +a+a +a=(+a) +a (-a, a) (-a, a) + --=0 (-a) +a - a-<0, a -a-<0 (a-)(a+)<0 -<a< a 0, 59 + =, =- (0, 0) ( + -)(--) (0+0-)(0-0-)>0 (0, 0) 550 =, + = (, 0) (-)( + -) (-0)(+0-)>0 (, 0) ( ) (-)( + -)æ0 55 =0, =0, -=0, +=0, + -=0 (, ) (-)(+)( + -) (-)(+)(+-)=-<0 (-)(+)( + -) 0 ( - )( + -) 0 55 =+a =+a+ A, =a-, =a- A(a-, a-) A + (a-) +(a-) 0a -8a- 0, 5a -a- 0 (5a+)(a-) 0 -;5!; a M=, m=-;5!; M-m=;5^; 55 + æ0, æ0, + -+ æ0, <0, - æ- <0, æ0, -+ + <0, <0, -- æ-- ( ), (, ) =k(k ) =;!;+;K; (7, ),k m=-7=-5 (5, ),k M=8-5=, M+m=- 555 ( ) - +=k(k ) = -+k =(-) +k- =, (, ), - +_=7 +-= =0 - = 78

179 0 ~ 0 (, 0), 0- +_=0, p + = (0, 0) +-a=0 ' -a " + =', -a = a= ( a>0) a aæ 557 ( ) -=k(k ) =;!;-;K; (, 0),k -0= (0, ),k 0-=-, +(-)= æ0 æ0, æ0 0, 0 ( ) + ( ) -5+0=0 +-=0 5 -;; k =;;-;; -' 5 -;; - ' -' +=a 5--0=0 ' + = =0, =0 + -=0 + = (0, 0) ', =0 (-) +(-) =8 (, ) ' (, ) (+-)(+---6)=-<0 {-}@+{-}@=8 (, ) Â p ('8) -p (') =6p 560 = + =k ( ) + =k(k>0) =-+ 'ßk (, 0),, 0, M=, m=0 M+m= 56 'ƒ+ 'ƒ-=-" (+ )( -Ω) +=0 -=0 +<0, -<0 -, æ =- ( ) = ( ) 56 (-) + r (-) + 9 r - r r -, -,, (-) + =9 - (-) + =r, ( ) _;!; = ABC AB =+, BC =, AC =-+ ABC A B - =+ C = =-+ 79

180 RPM <+, >, <-+ ( ) (a, a) ABC a<6a+ a>-;5$; a> a<-a+ a<;$;,, <a<;$; 56 ( ) - =k(k ) - -=k(-) k (, ) k (, 0),k 0- = - (0, ),k - =-;!; 0- _{-;!;}= =k(k ) -+ ++=k(-+) (-k)+(+k)+(-k)=0 + = (-k) " (- k) +( +k)ω (-k) " (- k) +( +k)ω (-k) (-k) +(+k) k -k+ 0 -' k +' k +', -' 566 A, B g, g +5(kcal), +(g) =-+ ( { æ0 æ0 500 ( ) 60 (50, 50) =800 +=500 +=k +=k(k ) +5=800, +=500 (50, 50), k A 50 g 567 -' +æ0, æ' - =' -( ), + + 0, +(+) +(+) = ( ) =' - ( ) ' AC= BC=0 ACB=60 p 60 p p_ = ( ) +=k(k>0) =-+k - ' B - C +(+) = =-+8 (, ) = =-+k A ' 0% ACB 0% 0% p 6 =-+ 80

181 0 ~ 05 (, ),k +=5 (, 0),k +0= + =k(k>0) =-+8 (, ) = + =k (, ),k + =7, +-=0,k - ='ßk k=: 5 : " + Ω, : 5 : 5, 569 [] -9[]+0=0 ([]-)([]-5)=0 []= []=5 <6 7, : 5 : [] -[]+=0 ([]-)([]-)=0 []= []= <, (, ) 6 (6-)(-)= =-+ +, 50% +, 50% 570,, A, B +5(kg), +(kg) ( { 9 0% 0%, 0% (, ) 0% +5 + æ0 æ0 ( ) 6+5=k(k ) +5=, += (7, ),k 7,, 6_7+5_=5() 7,, 5 57 {-f()}{-g()} 0 -f()æ0 -f() 0 [ [ -g() 0 -g()æ0 æf() f() [ [ g() æg() += +5= :5: 6+5=k æf() [ g() ( ) :: (7, ) 7 :: :: 0% 0%, 0% 8

182 RPM f() [ æg() ( ), ( ) ( ) + =k (k>0) (0, 0) - 'k + =k(, 7),k + = +7 = A, B f(, )=0 f(, )f(, )<0 A, D f(, )=0 f(, )f(, )>0 C f(, )=0 f(, )=0 f(, )f(, )=0 f(, )f(, )>0 A, DB f(, )=0 f(, )f(, )f(, )<0 f(, )=0 f(, )f(, )f(, )=0, - 7 -k ' + >, k >'5 k<-'5 k>'5 +-k=0 k k k>'5 575 =, =-+, = - (, 0) (-)(+-)( --) (-0)(+0-)(--0)>0 (, 0) ( ) A, C k>'5 576 A, B A(-, 0), B(, 0) P(, ) P, B AP >BP AP >BP (+) + >(-) <0 (-5) + <6 P (5, 0), B 6p=8(km ) A B D F C E G =9, +-kæ0 =-+k ( - (0, 0) +-k=0 k - =-+k 8

183 고등RPM수해(56~8) :5 PM MEM 페이지8 다민 50DPI 75LPI

184 고등RPM수해(56~8) :5 PM MEM 페이지8 다민 50DPI 75LPI