#고등수학Ⅰ기본서해답(001~080)

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2 0 I. 7A-3{B+(A-C)}-4C =7A-3(B+A-C)-4C =7A-3B-6A+3C-4C =A-3B-C =( ) -3( )-( ) = =(-7-9 )+(-4 +3 )+(3 +8 ) +(-4)+(4-3+) = A-B= +3-4 A+B= B=3-9+6 B= -3+ A=B+( +3-4) = =3-3A-B=3(3 -)-( -3+) = = _(-z) () =6 _4 z ( ) =(6_4)_ z =64z {;3@;a b}3 (a b) _{-;!;b }3 =; 7;afl b (afl b )_{-;8!;bfl } =[; 7;_{-;8!;}]_afl fl b ±fl =-; 7;b 64z -; 7;b 04 ( -+)(-3) = = (3+-4)(-+3) = = ( +a +b)( -3b+4) (-3b)+a =(a-3b) a 4+b =(4a+b) 8 a-3b=8, 4a+b=8 a=;%;, b=- a+b=;#; f()=( -+3)(5 - ++) f() f() f()=(-+3)(5-++) =0

3 ( )( ) 06 (-5 )+3 +(-5 ) (- ) + 3 = =6 6 +8, 8-6 ;#; , , , < < f()=( -)(+3)+3- = = + - f()=6+4-=9 9 A=( ) (3 --4) A < A= (3a-b) =(3a) - 3a b+(b) =9a -ab+4b {;3@;a-;#;b}{;3@;a+;#;b} ={;3@; a} -{;#; b} =;9$;a -;4(;b (-)(-5) = +(--5)+(-) (-5) = -7+0 (+3)(-5) = +{ (-5)+3 }+3 (-5) = (-)(-3)(-4) = -(+3+4) +( )- 3 4 = (a-b)(a+b)(a +b )(a +b ) =(a -b )(a +b )(a +b ) =(a -b )(a +b ) =a -b =A(3 --4)+5-8 A(3 --4)= a -ab+4b ;9$;a -;4(;b a -b 3

4 0 (-++3z) =(-) +() +(3z) + (-) =+ 3z+ 3z (-) = +4 +9z -4+z-6z (5+3) =(5) +3 (5) (3) +(3) = (-3)( ) =(-3){() + 3+(3) } =() -(3) =8-7 (a -5bc)(a +5bc) =(a ) -(5bc) =a -5b c ( +3+9 )( -3+9 ) ={ + 3+(3) }{ - 3+(3) } = + (3) +(3) = z -4+z-6z a -5b c ( +5-)( +5-3) =(X-)(X-3) +5=X =X -5X+6 =( +5) -5( +5)+6 = = (a+b-c)(a-b+c) ={a+(b-c)}{a-(b-c)} =(a+x)(a-x) b-c=x =a -X =a -(b-c) =a -b -c +bc (+)(+5)(-)(+9) ={(+)(+5)}{(-)(+9)} =( +7+0)( +7-8) =(X+0)(X-8) +7=X =X -8X-80 =( +7) -8( +7)-80 = = (-)(-)(-3)(-4) ={(-)(-4)}{(-)(-3)} =( -5+4)( -5+6) =(X+4)(X+6) -5=X =X +0X+4 =( -5) +0( -5)+4 = = a -b -c +bc (-) (+3) =( )(4 ++9) (-6 ) 9+ +(-8) 4 = = (3 -+)fi = (3-+)fi =fi =

5 4 ( ) =( )( ) fi (-) 3 + (-3 )+(-3 ) +3 (-) =-3fi -6fi -6fi -3fi =-8fi fi (3+)(3 +)(3 +)(3 +) =;!;(3-)(3+)(3 +)(3 +)(3 +) ;!;(3-)= =;!;(3 -)(3 +)(3 +)(3 +) =;!;(3 -)(3 +)(3 +) =;!;(3 -)(3 +) =;!;(3 fl -) ;!;(3 fl -) 6 a +b =(a+b) -ab 3=6 -ab ab= (a-b) =(a+b) -4ab=6-4 =8 a-b= '7 '7 7 ='+, ='- +=', = = 5 (+) -3(+) = (') -3 ' = =0' 0' 8 + =(+) -3(+) 4= -3 =- ++ =(+) - = -(-) = 9-3 ={-;[!;}3 +3{-;[!;} =3 +3 3= '5+=0 +0 -'5+;[!;=0 +;[!;='5 + 3 ={+;[!;}3-3{+;[!;} =('5) -3'5='5 '5 -=+'3, -z=-'3 -z=4 z-=-4 + +z --z-z =;!; {(-) +(-z) +(z-) } =;!; {(+'3) +(-'3) +(-4) } =5 5 (a+b+c) =a +b +c +(ab+bc+ca) =8+(ab+bc+ca) ab+bc+ca=- ab+bc+ca ;a!;+;b!;+;c!;= 5443 abc - = 5 =- - 5

6 3 a +b +c =(a+b+c) -(ab+bc+ca) = - (-) =6 a +b +c =(a+b+c)(a +b +c -ab-bc-ca)+3abc = {6-(-)}+3 (-) =8 a +b +c =(a +b +c ) -(a b +b c +c a ) (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 =9 a +b +c =6-9= =a +(b-a) +(c-b)-c a=, b-a=0, c-b=-, -c= a=, b=, c=- a=, b=, c=- 5 =a(-)(-)(-3)+b(-)(-) +c(-)+d = =d = 8=c+d =3 7=b+c+d =4 64=6a+6b+3c+d,,, a=, b=6, c=7, d= a=, b=6, c=7, d= 6 (+)( -)f()= +a -b =- 0=+a-b = 0=4+a-b, a=-3, b=- a+b= k (+)k+(--)=4k+ k +=4, --= =-5, =9 =-5, =9 8, (a+b)+(a-b)+=3-5+c, a+b=3, a-b=-5, =c a=-, b=4, c= abc= a +b+ +-3 Q() + +a +b+ =( +-3)Q()++ =(+3)(-)Q()++ 6

7 =-3-7+9a-3b+=-5 9a-3b=0 = +a+b+=3 a+b=0, a=;3%;, b=-;3%; +a-8 +4+b +q(q ) 0 +a-8=( +4+b)(+q) = +(q+4) +(b+4q)+bq q+4=0, b+4q=a, bq=-8 q=-4, a=-4, b= a=;3%;, b=-;3%; a=-4, b= 30 f()=3 +a +b- f{;3@;}=0, f(-)=-0 f{;3@;}=0 ;9*;+;9$;a+;3@;b-=0 a+3b=5 f(-)=-0-3+a-b-=-0 a-b=-5, a=-8, b=7 a=-8, b=7 3 f()= +a +5-6 f()= f(3) 8+4a+0-6=7+9a+5-6 a=-: 5 : -: 5 : 3 f()=3 +a +b+ f() -5+6, (-)(-3) f()=0, f(3)=0 f()=0 4+4a+b+=0 a+b=-8 f(3)=0 8+9a+3b+=0 3a+b=-3, a=-3, b=8 a=-3, b=8 33 f() -4-, (+)(-6) Q(), a+b(a, b ) f()=(+)(-6)q()+a+b f(-)=-a+b=6 f(6)=6a+b=-0, a=-, b= f() (-)(-)(-3) Q(), a +b+c(a, b, c ) f()=(-)(-)(-3)q()+a +b+c f()=a+b+c=5 f()=4a+b+c=9 f(3)=9a+3b+c=47,, a=7, b=-47, c= f() (-) (-3) Q(), a +b+c(a, b, c) 7

8 f()=(-) (-3)Q()+a +b+c f() (-) a +b+c (-) a +b+c=a(-) f()=(-) (-3)Q()+a(-) f() -3 5 f(3)=4a=5 a=;4%; ;4%;(-) ;4%;(-) 36 f() ( +)(-) Q(), a +b+c(a, b, c) f()=( +)(-)Q()+a +b+c f() + + a +b+c + + a +b+c=a( +)++ f()=( +)(-)Q()+a( +)++ f() - 4 f()=a+=4 a= ( +)++= =3 f(3)=4 3-= f()=(+)(-3)q()+4-3 f(3)=(6+)(3-3)q(3)+- f(3)=3(6+)(-)q(3)+(-)+ f(3)=(-){3(6+)q(3)+}+ f(3) - 38 f() - 4 f()=4 f(-3) -5 Q(), R f(-3)=(-5)q()+r =5 R=5f()=5 4= f()=(-3)q()+4 Q() - Q'() Q()=(-)Q'()+ f()=(-3){(-)q'()+}+4 f() - f()=(-3) +4= 37 f(3) - f(3 )=f(3) f() -5-3 Q() f()=( -5-3)Q()+4-40 f()= +a ++b f() -, - f()=0, f()=0 f()=0 +a++b=0 a+b=-3 8

9 f()=0 6+4a++b=0 4a+b=-8, a=-5, b= a +b =(-5) + =9 9 4 f()= - +a+b f() --, (-)(+) f()=0, f(-)=0 f()=0 8-4+a+b=0 a+b=-4 f(-)=0 ---a+b=0 a-b=-, a=-, b=0 a+b=- - 4 ;#;f f ;#;f ={-;#;}( +8-)+ ={-;#;} ( +4-)+ =(-3)( +4-)+ +4-, fi +=(+)( ) , 0 +4-, , d 5 c 3 b a a=, b=3, c=5, d= d c - - b a a=, b=, c=-, d=-7 a+b+c+d=-5 a=, b=3, c=5, d=7 = =a(3-) +b(3-) +c(3-)+d a+b+c+d= a b-6ab =3ab(a -b) -5 (+) -5(+)=(+)(+-5) (-)-+=(-)-(-) =(-)(-) 9

10 46 +=( +) =(+)( -+) - =( ) -( ) =( + )( - ) =( + )(+)(-) 3(4-) -=3{(4-) -4} =3{(4-)+}{(4-)-} =3(4+)(4-3) 9(a+b) -c ={3(a+b)} -c ={3(a+b)+c}{3(a+b)-c} =(3a+3b+c)(3a+3b-c) +64 = +(4) =(+4)( -4+6 ) (a+b) -(a-b) ={(a+b)-(a-b)} _{(a+b) +(a+b)(a-b)+(a-b) } =b(3a +b ) - =( ) -( ) =( + )( - ) =( + )( + )( - ) =( + )( + )(+)(-) -=( ) - =( +)( -) =( +)(+)(-) 47 +=X (+) -(+)z-z =X -Xz-z =(X-z)(X+z) =(+-z)(++z) a+5=a, a-3=b (a+5) -5(a+5)(a-3)+3(a-3) =A -5AB+3B =(A-3B)(A-B) ={(a+5)-3(a-3)}{(a+5)-(a-3)} =-8(a-9) (+-z)(++z) -8(a-9) 48 a -ab -b c+a c=(a -ab )+(-b c+a c) =a(a -b )+c(a -b ) =(a -b )(a+c) =(a+b)(a-b)(a+c) -a +-4a=( -a )+(-4a) = (-a)+(-a) =(-a)( +) 4ab+-4a -b =-(4a -4ab+b ) =-(a-b) =(+a-b)(-a+b) =(+) - =(++)(+-) =() -3 () +3 - =(-) =X +X-6 =X =(X+3)(X-) =( +3)( -) -3 +4=( -4 +4)-9 =( -) -(3) =( +3-)( -3-) =X -3X+36 =X =(X-4)(X-9) =( -4)( -9) =(+)(-)(+3)(-3) +4=( +4 +4)-4 =( +) -() =( ++)( -+) +5 +9=( +6 +9)- =( +3) - =( ++3)( -+3) 0

11 6 - - =4 -( - + ) =() -( - ) =(+ - )(- + ) =-( +- )( -- ) =( - +36)- =( -6) - =( +-6)( --6) =(+3)(-)(-3)(+) 50 ( +) -3( +)+36 =X -3X+36 +=X =(X-4)(X-9) =( +-4)( +-9) (+)(+)(+3)-5 ={(+3)}{(+)(+)}-5 =( +3)( +3+)-5 =X(X+)-5 +3=X =X +X-5 =(X+5)(X-3) =( +3+5)( +3-3) (+)(+)(+3)(+4)+ ={(+)(+4)}{(+)(+3)}+ =( +5+4)( +5+6)+ =(X+4)(X+6)+ +5=X =X +0X+5=(X+5) =( +5+5) (-- )(-+3 )+4 =(X- )(X+3 )+4 -=X =X + X-3 +4 =X + X+ =(X+ ) =(-+ ) ={(-) } =(-) ( +4+3)( ++35)+5 =(+)(+3)(+5)(+7)+5 ={(+)(+7)}{(+3)(+5)}+5 =( +8+7)( +8+5)+5 =(X+7)(X+5)+5 =X +X+0 =(X+0)(X+) =( +8+0)( +8+) =( +8+0)(+)(+6) 5 a a (b-c)+b (c-a)+c (a-b) =(b-c)a -(b -c )a+b c-bc +8=X =(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+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) =(a+b)(b+c)(c+a) = +(+)-(6-3+6) = +(+)-(-3)(3-) -(3-) -3- -(-3) ={+(3-)}{-(-3)} =(+3-)(-+3) z - +z+z+4++z+3

12 =(++)z =(++)z+ +4-( --3) =(++)z +{ +4-(+)(-3)} -(+) -+ -(-3) =(++)z+(++)(-+3) =(++)(-+z+3) 5 78= 78_79 (+) (+) 3 = 3 = (-)(+) 78 = 33 = 3 =;7&7*; = = _003+4 (-)+4 (+)( -+4) = =+=005+ = =(0 - )+(4-6 )+(8-0 ) =(0-)(0+)+(4-6)(4+6) +(8-0)(8+0) =-(+30+38) =-_90= ;7&7*; a -a b+ab +ac -b -bc =0 c (a-b)c +a -a b+ab -b =0 (a-b)c +a (a-b)+b (a-b)=0 (a-b)(c +a +b )=0 a +b +c +0 a-b=0 a=b a=b a=b = { +3-8+;[#;+ 3 } = [{ + 3 }+3{+;[!;}-8] = [{+;[!;} +3{+;[!;}-0] +;[!;=t {+;[!;} +3{+;[!;}-0 =t +3t-0=(t+5)(t-) ={+;[!;+5}{+;[!;-} ( )= {+;[!;+5}{+;[!;-} ( )={+;[!;+5} {+;[!;-} ( )=( +5+)( -+) ( )=( +5+)(-) = { +++;[!;+ 3 } = [{ + 3 }+{+;[!;}+] = [{+;[!;} +{+;[!;}-3] +;[!;=t {+;[!;} +{+;[!;}-3 =t +t-3=(t-)(t+3) ={+;[!;-}[{+;[!;}+3] ( )= {+;[!;-}[{+;[!;}+3] ( )={+;[!;-} {+;[@;+3} ( )=( -+)( +3+)

13 55 f()= f(-)=0 f() + f() f()=(+)(3 +4-4) =(+)(+)(3-) (+)(+)(3-) 56 f()= f()=0, f(-)=0 f() -, + f() f f()=(-)(+)( -3+) (-)(+)( -3+) 57 f()= -6 -a-6 f() - f()=8-4-a-6=0 a=- f()= f() f()=(-)( -4+3) =(-)(-)(-3) (-)(-)(-3) 58 II. a+bi a=0, b+0 ' -6=4i, '3i 59 ' -= 'i ' -9= '9i= 3i ' -4= 'ß4i= '6i ' -6, '3i 'i 3i '6i 60 3+i ;!;-;3@;i +'5 i 6 (4+3i)-(-5i)=(4-)+(3+5)i =+8i (+'i)(-'i)=-'i+'i-i =-'i+'i+ =4+'i (+'5i) =4+4'5i+5i =4+4'5i-5 =-+4'5i (+i) +(-i) =(+i+i )+(-i+i ) =+i-+-i-=0 4+i (4+i)(+3i) 3= -3i (-3i)(+3i) 8+i+i+3i 5+4i = 5= 5 4-9i = i 3 3 -i +i i -i (-i)(-i) = 5+ (+i)(+i) (+i)(-i) (-i)(+i) 3

14 -i-i+i +i+i+i = i -i --3i +3i = + =0 +8i 4+'i -+4'5i 0 ; 3;+;!3$;i 0 6 (+i)(3+i)=-8+i 6+4i+3i+i =-8+i (6-)+(4+3)i=-8+i 6-=-8, 4+3= =-, =- (-i)+(+i) 3+ 3= 5 +i -i (+i)(-i) + -+ = i i=-3i =, 35 =-3 +=, -+=-6 =4, = = +3i -3i +i (-3i)+(+3i) 9(-i) 5= (+3i)(-3i) (+i)(-i) i= 3- i = 3 = =36-=6 ==5 (4+i)+ (-3i)=-3i (4+) +(-3)i=-3i (4+)-(-3)i=-3i 4+=, -3=3 =;7^;, =-;7%; =-, =- =4, =- =, =5 =;7^;, =-;7%; 63 aa -ab -a b+bb =a(a -b )-b(a -b ) =(a-b)(a -b ) =(a-b)(a-b) =(4+'5i)(4-'5i) =6+5 = 64 z=+i z =-i z-z =(+i)-(-i)=i zz =(+i)(-i)= zz = 3= =-i -i z-z i i 65 z=a+bi(a, b ) z =a-bi iz+(-i)z =i i(a+bi)+(-i)(a-bi)=i ai-b+a-bi-ai-b=i (a-b)-bi=i a-b=0, -b= a=-4, b=- zz =(-4-i)(-4+i) zz =6+4 zz =0 0 4

15 66 z=(+i) -3+-i z=( -3+)+( -)i z ()= -=0 = z=a -a-+(a+)i ()=0, ()+0 ()=a -a-=0 (a+)(a-)=0 a=- a= ()=a++0 a+-, a= 68 3+'7i z= z=3+'7i z-3='7i 4z -z+9=-7, z -3z+4=0 z =3z-4 z =z(3z-4)=3z -4z z =3(3z-4)-4z z =5z- z -z +z- =(5z-)-(3z-4)+z- =-6-6 z -z +3z -z+ =z (z -z+)+z -z+ =z (z -z+)+(z -z+)- =z 0+0-= i+i +i +i =i--i+=0 +i+i +i ++i =+(i+i +i +i )++i (i+i +i +i ) = i+i +3i ++0i =i--3i+4+5i-6-7i+8+9i-0 =( )+( )i =-6+5i = -- +=0 i i i i i i i i i i i ={ }+ i i i i =+ 55{ }+ 55 i i i i i i = 55 = = =-i i (i )fi i i +i (+i) i 55= 5 = 55 =i -i (-i)(+i) -i (-i) -i 55= = =-i +i (+i)(-i) +i { } -i 55 +{ 55} =i +(-i) -i +i ( ) =(i ) fi +{(-i) } fi ( ) =+= -6+5i -i 69 z=-i z-=-i z -z+=- z -z+=0 7 -i (-i) -i 55= 3= 5 =-i +i (+i)(-i) -i { 55} =(-i) =i =- +i 5

16 -i { 55}4 =(-) = +i -i { 55}n= n +i 'ƒ-4 3+'ƒ-9 + +'ƒ-4 3-'ƒ-9 -'4i 3+'9i = '4i 3-'9i -i 3+3i = i 3-3i -i +i = i -i (-i) +(+i) = (+i)(-i) -i+i = =0 ' 'ƒ- 'ƒ-3' +'ƒ-3'ƒ-+ + 'ƒ-3 'ƒ-3 '3 '3i ='3i '3+'3i '3i+ + '3i '3i =6i-6+ + i =6i-6-i+ =-4+4i 0-4+4i 73 'ƒ =-æ 'ƒ >0, -3-<0 7-=0-3< ;&; -, -, 0,,, 'ƒa-4'ƒ-a=-" (a-4)(-a) a-4<0, -a<0 a-4=0 -a=0 a 4 " (a+3) - -a = a+3 - -a =a+3-{-(-a)} =a+3+-a=4 4 KEY Point aæ0 a a =[, "ça = a a<0 -a 75 (a +6)=a(5+)- (a -5a+6)=a- (a-)(a-3)=a- 0 =(0 ) (a-)(a-3)=0, a-+0 a= a+9=a +3 (a-3)=a -9 (a-3)=(a+3)(a-3) 0 =0 a-3=0, (a+3)(a-3)=0 a= (m+)(m-)=3+m- (m --3)=m- (m+)(m-)=m- 0 =0 (m+)(m-)=0, m-=0 m= m= (m-)+m=0 +4=0 =-4 =-4 6

17 =0-3 = 4- -3= (4-) -3=4-,=;&; -3=-(4-), 0 =-, =;&; 0 -=0, +=0 =, =- <-, -<0, +<0 -(-)+3(+)=-9 0 =-4 - <, -<0, +æ0 -(-)-3(+)=-9 =;3$; æ, -æ0, +>0 (-)-3(+)=-9 = æ =,, =;3$; - = -3 -= (-3) -=-3, = -=-(-3), =0, =0 = 0-6=0, +3=0 =3, =-3 <-3, -6<0, +3<0 -(-6)+(+3)= =8 <-3 =8-3 <3, -6<0, +3æ0 -(-6)-(+3)= =;3@; æ3, -6æ0, +3>0 (-6)-(+3)= =0,, =;3@; =0 =;&; =;3$; =0 = =;3@; =0 0-3=0, 4-=0 =3, =4 <3, -3<0, 4->0 -(-3)-(4-)=0, 0 = 3 <4, -3æ0, 4->0 (-3)-(4-)=0 =;&; æ4, -3>0, 4-0 (-3)+(4-)=0, 0 =-,, =;&; 79-5+=0 (-)(-)=0 =;!; = (+)=3(+) (+)-3(+)=0 (+)(-3)=0 =- =3 =;!; = =- =3 80 (-)(-3)= -8 ( -4+3)= -8 7

18 -8+4=0 -(-4) " (-4) - 4 = 5=4 ' 3-4+6=0 -(-) "( -)ç -3 Ω6 = 5 3 'ƒ-4 = 3 3 ' 4 i = 5 3 ' 4 i =4 ' = (a+)+a=0 =3 9-3(a+)+a=0 a=3 a=3 +a-a -=0 +3-0=0 (-)(+5)=0 = =-5 = =-5 8 +k-k-=0 =k k +k -k-=0 3k -k-=0 (k-)(3k+)=0 k= ( k>0) 83 -'3 (-'3)(+'3) -(-'3)(3+'3) +-'3=0 -(3-'3)+-'3=0 (-){-(-'3)}=0 = =-'3 = =-' =3 <;!;, - =-(-) -(-)=3, --=0 = '3 <;!; =-'3 æ;!;, - =- +-=3, +-4=0 =- '5 æ;!; =-+'5, =-'3 =-+' =0 <0, =- +-80=0, (+0)(-8)=0 =-0 =8 <0 =-0 æ0, = --80=0, (-0)(+8)=0 =0 =-8 æ0 =0, =-0 =0-3-= - <, - =-(-) -3-=-(-) --3=0, (-3)(+)=0 =3 =- < =- æ, - =- -3-=-, -4+=0 = '3 æ =+'3, =- =+'3 =-'3 =-+'5 =-0 =0 =- =+'3 8

19 85 [] -[]+3=0 ([]-4)([]-8)=0 []=4 []=8 []=4 4 <5 []=8 8 <9 4 <5 8 <9 [] -[]-=0 ([]+)([]-)=0 []=-;!; []= [] []= < -+[]=0 0 <, []=0 -=0, (-)=0 =0 = 0 < =0 <, []= -+=0, (-) =0 = <3, []= -+=0 = i <3,, =0 = 3 +[]-=0 -<<0, []=- 3 --=0, (3+)(-)=0 =-;3@; = -<<0 =-;3@; 0 <, []=0 '6 3 -=0 = 3 '6 0 < = 3 '6, =-;3@; = 3 86 ;!; 3 ;!;(+3)(+) ( ) =( ) ;!;(+3)(+)=_;!; -5-6=0, (+)(-6)=0 =6 ( >0) ;!; =;!;_6 = m 0 m m 0 m (0-)m (0-) m m m 44 m (0-)(0-)= =0(-)(-8)=0 = ( 0<<0) m m 88 (k-) +k+k-=0 k-+0 k+ D ;;4;D;=k -(k-) >0 9

20 k->0 k>;!;, ;!;<k< k> ;!;<k< k> 89 -(k-4)-=0 (-k) +4-=0 -k+0 k+ D ;;4;D;= -(-k) (-)<0 -k+5<0 k>5, k>5 k k-=0 D D =(-) -3(-k-)æ0 4 6k+4æ0 kæ-;3@; -(k-)+k -5k+4=0 D D =(k-) -(k -5k+4)<0 4 3k-3<0 k<, -;3@; k< -;3@; k< 9 +(k+)+k -k+=0 D, D=(k+) -4(k -k+)=0 9 +(k+a)+k +6k+b=0 D=0 ;;4;D;=(k+a) -(k +6k+b)=0 (a-6)k+a -b=0 k a-6=0, a -b=0 a=3, b=9 a+b= =0 a, b a+b=;3$;, ab=-;3@; a +b =(a+b) -3ab(a+b) a +b ={;3$;}3-3 {-;3@;} ;3$;=: 7 : b a b +a = 3 a b a b (a+b) -3ab(a+b) = (ab) : 7 : = 3 =: 3 : {-;3@;} (a-b) =(a+b) -4ab (a-b) ={;3$;} -4 {-;3@;} (a-b) =: 9 :+;3*;=: 9º: (a-)(b-)=4ab-(a+b)+ =4 {-;3@;}- ;3$;+ =-;3*;-;3*;+=-: 3 : (a-3b+)(b-3a+) =0ab-3(a +b )-(a+b)+ =0ab-3{(a+b) -ab}-(a+b)+ 8k-7=0 k=;8&; ;8&; =0 {-;3@;}-3[{;3$;} - {-;3@;}]- ;3$;+ 0

21 =-: 3º:-3 : 9 :-;3*;+ =-;; 3 ;; : 7 : : 3 : : 9º: -: 3 : -: 3 : 94 +a+b=0 a, b a+b=-a, ab=b -a-b=0 a-, b- (a-)+(b-)=a, (a-)(b-)=-b a+b-=a ab-(a+b)+=-b -a-=a, b+a+=-b a=-, b=0 a=-, b=0 95 a, a+ a+(a+)=-m a(a+)=5 a +a-5=0 (a-3)(a+5)=0 a=3 a=-5 a=3, m=-4 a=-5, m=4 m=-4 m=4-4 4 " (m) -4 5= 4m -60=4, m =6 m= a, 3a(a+0) a+3a=a+ a 3a=a a=3a 4a=3a +, 3a -4a+=0 (3a-)(a-)=0 a=;3!; a= a=;3!;,a=;3!; a=,a=3 a=;3!; a=3 ;3!; 3 -(a+)+a=0 (-)(-a)=0 = =a 3 a=3 a=;3!; 97 :5 a, 5a(a+0) a+5a=7 a 5a=k, a=, k=0 k=0 +k-k+3=0 +0-7= ('-' )+' (-' )=0 -=0 -(+3i+-3i)+(+3i)(-3i)=0-4+3=0 +3'i -3'i -{ + } +3'i -3'i + =0 -+: :=0

22 99-5+4=0 a, b a+b=;%;, ab= a+, b+ (a+)+(b+)=a+b+=;%;+=;(; (a+)(b+)=ab+a+b+ (a+)(b+)=+;%;+=;; ;; a+, b+ { -;(;+;; ;;}=0-9+=0-9+= =0 a, b a+b=3, ab= a +;!;, b +;å!; {a +;!;}+{b +;å!;}=a +b +;!;+;å!; a+b {a +;!;}+{b +;å!;}=(a+b) -ab+ ab {a +;!;}+{b +;å!;}=3 - +3=0 {a +;!;}{b +;å!;}=a b +a+b+ 5 ab = +3+=5 a +;!;, b +;å!; -0+5=0-0+5=0 0 +a-b=0 a, b '+ -' ('+)+(-')=-a a=- ('+)(-')=-b b= ab= a+b=0 a, b +3i -3i (+3i)+(-3i)=-a a=-4 (+3i)(-3i)=b b=3 a=-4, b= a=0 b+'3i b-'3i (b+'3i)+(b-'3i)=-6 b=-3 (b+'3i)(b-'3i)=a a= a+b= =0 = '5-5=(-'5 )(+'5) +6+4=0 =-3 ' ={-(-3+'5)}{-(-3-'5)} =(+3-'5 )(+3+'5) '5i 3 -+=0 = '5i -'5i =3 {- }{- } f()=0 a, b f(-)=0

23 -=a -=b a+ b+ = 3 = 3 f(-)=0 a+ b+ ab+(a+b)+ 3 3 = = 5 = 4 06 (m +) +4(m+)+4=0 a, b, D ;;4;D;={(m+)} -4(m +)æ0 08 +(a -a-)-a+3=0 a, b a, b ab=-a+3<0 a>3 a+b=-(a -a-)=0 (a+3)(a-4)=0 a=-3 a=4, a a+b+c=0 =-;ba;-;bc; 8mæ0 mæ0 4(m+) a+b=- 45 <0 m + m +>0-4(m+)<0 m>- 4 ab= m +>0 m + ab>0 m,, mæ0 a, b ab=a+<0 a<- mæ0 a<- ()=-;ba;<0 ;ba;>0 ()=-;bc;<0 a-b-c=0 =;ba;-;bc; ()=;ba;>0, ()=-;bc;<0, O a-b-c=0, 3, (k-7)-k+4=0 a, b ab=-k+4<0 k>4 a+b=-(k-7)>0 k<7, k 4<k<7 4<k<7 0 a+b+c=0 =-;ba;-;bc; a>0, b>0, c<0 ()=-;ba;<0, ()=-;bc;>0, O 3 3 3

24 f()=;3!;+a =f() b -3 O f(-3)=, f(9)=b -+a= a= 3+a=b b=5 9 a+b=7 7 f()=-+k =f() -4 =, =-4-4 O f()= k=-3 k=- f()=-- f(-4)=8-=7 7 f(-4) 3 - O - - =4 æ0, æ0, -=4 =-4 æ0, <0, +=4 =-+4 <0, æ0, --=4 =--4 <0, <0, -+=4 =+4 O =3 -+ æ0, =3-+ =+ <0, =-3-+ =-4+ - =+ æ, -=+ =+3 <, -+=+ =-- O 4 + =6 æ0, æ0, +=6 =-+6 æ0, <0, -=6 =-6 <0, æ0, -+=6 =+6 <0, <0, --=6 =--6 + =6 4 {;!; 3 6}= O 3-6 4

25 5 = f() =f( ) <-, =-(+)-(-)-5 =--4 - <, O O =(+)-(-)-5 =- æ, = f() = f( ) =(+)+(-)-5 =-6 O O - - O = - = - =-, O = - =-, - O - = - =- æ0, æ0,,, - O 7 = , = , <-, =-(-)+(+) =4 - <, =-(-)-(+) =- æ, =(-)-(+) =-4 4 = O = , 4 - O 5

26 8 =- - <, =+(-)=3- æ, =-(-)=-+, - =- - = M= =- m=-8 - O - -8 M+m= = , 3 <-, =-(+)-(-3)=-+ - <3, =(+)-(-3)=5 æ3, =(+)+(-3) =- 5 = O ;3{;<-, -6 <-3, =[;3{;]=- - ;3{;<0, -3 <0, =[;3{;]=- 0 ;3{;<, 0 <3, =[;3{;]=0 ;3{;<, 3 <6, =[;3{;]= =[;3{;] -6-3 O <-, []=- =-4 - <0, []=- =- 0 <, []=0 =0 <, []= = 4 fi =, []= = O - =[] -4-3<<-, []=-3 =-3+ - <-, []=- =-+ - <0, []=- 0 =-+ 0 <, 7 []=0 = 5-3<< 3 =[] O =[] 6 6

27 = --3 =(-) -4 (, -4) = =0 --3=0 (+)(-3)=0 -, 3 =0 =-3-3 =-;!; +=-;!;( -4) =-;!;(-) + (, ) = =0-4=0 (-4)=0 0, 4 =0 =0 0 = - (0, -) =0 =0 - -=0 (+)(-)=0 -, =0 =- - = +4+ =(+) (-, 0) =- =0 (+) =0 - - =0 = O O 4 O - 3 O = -3 = '3 O '3-3 = =- + =- + =- +, - - O = -4 = -4, O a>0 -;ıa;>0 b<0 c>0 = <0 a+b+c<0 =- >0 a-b+c>0 =- >0 4a-b+c>0 a>0 b<0 c>0 a+b+c<0 a-b+c>0 4a-b+c>0 7

28 4 = -k+k -k+3 =(-k) -k+3 (k, -k+3) =-+ -k+3=-k+ k= 5 = -k+k +k- =(-k) +k- (k, k-) k>0, k->0 k>0, k> k> k> 6 (-, 3) =a(+) +3 (, -6) -6=9a+3 a=- =-(+) +3 =- -4- =a +b+c (-, 6) 6=a-b+c (, -6) -6=4a+b+c (3, ) =9a+3b+c,, a=3, b=-7, c=-4 =3-7-4 = =a(-) +b (, 0) 0=a+b (, -) -=b, a=, b=- =(-) -= -4+3 =a(-p) (, ) =a(-p) (4, 4) 4=a(4-p) (4-p) 4-p 4= 3 ={ } (-p) -p 4-p 4-p =- = -p -p p= p=- a= a=;9!; p=, a= p=-, a=;9!; =(-) =;9!;(+) =- -4- =3-7-4 = -4+3 =(-) =;9!;(+) 7 = +a-3a a (-3)a+ -=0 a 8

29 -3=0, -=0 =3, =9 (3, 9) =(-3) +9 = -6+8 a= =- + = - (0, -) (0, -) 9 = -+k -+k=0 D>0 ;;4;D;=(-) -k>0 k< k< 30 =a -8+a+6 a -8+a+6=0 D=0 ;;4;D;=(-4) -a(a+6)=0 a +6a-6=0, (a+8)(a-)=0 a=-8 a= a +b =(-8) + = = - -=0 -=0 = = ' (-', 0), (', 0) = =0 --=0 = ' (-', 0), (+', 0) (-', 0), (', 0) (-', 0), (+', 0) 3 = +a-4 -, b +a-4=0 -, b -+b=-a, - b=-4 a=-3, b=4 a+b= 33 = ++k a, b(a<b) a, b ++k=0 a+b=-, ab=k 4 b-a=4 (b-a) =6 (a+b) -4ab=6 (-) -4k=6 k=-3-3 = ++k=(+) +k- =- A, B AB =4 A(-3, 0), B(, 0) A - B -3 O 9

30 ++k=0-3, (-3) =k k= = =0 D ;;4;D;=(-) - 9=-8<0 35 = +-3 =k-k +-3=k-k, +(-k)-3+k=0 D D=(-k) -8(-3+k)=0 k -0k+5=0 (k-5) =0 k= =3+k = -+ 3+k= -+, -4+-k=0 D D =4-(-k)>0 4 k+>0 k>- =3+k = k= -+5, -4+5-k=0 D D =4-(5-k)<0 4 -+k<0 k<, -<k< k 0 37 = ++3 =3+k ++3=3+k, -+3-k=0 - = k=0 k=5 k=5 --=0 --6=0, (-3)(+)=0 =3 =- 3 (3, 4) (3, 4) 38 = -3+ =a+b -3+=a+b, -(3+a)+-b=0 -, 5 3+a -b -+5=, - 5= a=3, b= a+b= = -a+b =- -a+b=-, -(a+)+b+=0 a, b -'3 +'3 30

31 (-'3)+(+'3)=a+ (-'3)(+'3)=b+ a=, b=0 a+b= 40 = -4+ =-+0-4+= =0, (+)(-4)=0 =- =4 =- =4, =4 = (-, 4), (4, ) " (4+) + (-4) =' 80=6'5 6'5 4 = -5+ =+k (a, a+k), (b, b+k) -5+=+k, -6+-k=0 a, b a+b=6, ab=-k 4'3 " (a-b) +{a+ k-(b+k)} =4'3 " (a-b) =4'3 (a-b) =4 (a+b) -4ab=4 6-4(-k)=4 4k=-8 k=- - 4 =-+ - =-+b =-+b = =-+b, -+b-=0 D ;;4;D;=-(b-)=0 b= =-+ =-+ 43 =m+b (-, ) =-m+b b=m+ =m+m+ = =m+m+, +(6-m)-m+4=0 D D=(6-m) -8(-m+4)=0 m -4m+4=0, (m-) =0 m= =+3 =+3 44 =f() (-0) (3, 0) f()=a(+)(-3)(a<0) f(+p)=a(+p+)(+p-3) f(+p)=0 =-p- =-p+3 f(+p)=0 3 (-p-)+(-p+3)=3 p=-;!; -;!; =k = -4+3 =k 3

32 k= 3 k= = =k O 3 49 = =-4{-;!;} +4 ;!; - 3 =-, =-5 46 f() = f()=a(-) +(a>0) f(-)=4 4a+=4 a=;4#; f()=;4#;(-) +=;4#; -;#;+;4&; b=-;#;, c=;4&; a+b+4c= ;4#;+{-;#;}+4 ;4&; a+b+4c= = =-(-) + =- ++ a=, b= a=, b= a+b= =;!;, =4 =3, =- 4, - = -- ={-;!;} -;4%; ;!; 3 =, =- =3, =5 5, - 4, - 5, - 50 =-3 ++ =-3{-;3!;} +;3$; ;3!; 0 48 =a ++4+a =a{+;a!;} -;a!;+4+a 3 a<0, -;a!;+4+a=3 =0, = =;3!;,=;3$; =,=0 M=;3$;, m=0 M+m=;3$; ;3$; a +a-=0 (a-)(a+)=0 a=;!; a=- a<0 a=- - 5 =;3!; -+k =;3!;(-3) -3+k 3

33 , =3-3+k -3+k=- k= =;3!;(-3) - =-3, = =4, =-;3@; -3 O f()=- +k=-(-k) +k (kk ) kæ, =k 8, f(k)=8 k =8 k= ' kæ k=' k<, = O k 8, f()=8-4+4k=8 k=3 O k k=3 k<, k=' ' 0 a, =a 5 f(a)=+5 0 a a a>, = 5, f()=5 -a+a +=5 a -a-3=0 (a-3)(a+)=0 a=3 a=- a> a=3 O a,, a=- a=3 a -+3= =4( -4+4)+( ++)-6 =4(-) +(+) -6, (-) æ0, (+) æ æ-6 =, = f()= -a+a +=(-a) + =-( +4+4)-( -+)+7 (a, ) =-(+) -(-) +7 a<0,, (+) æ0, (-) æ0 = , f(0)=5 a +=5 a= a O =-, = 7 a<0 a=- 7 33

34 56 --=0 =- - - = -(-) =- +4- =-(-) + = 57 +4=t t= +4=(+) -4 tæ-4 =t -t-5 =(t-) -6 (tæ-4) t= =( +4+5)( +4+) =( +4+5)( +4+)+3( +4)+5 +4=t t= +4=(+) -4 tæ-4 =(t+5)(t+)+3t+5 =t +0t+5 =(t+5) -0 (tæ-4) t= =t t= ++ t t= ++ 5 =(+) t 5-3 -O =t -4t- =(t-) -5 ( t 5) t=5 4 t= -5 4+(-5)=- 60-0, +0 =(+0)= +0 =(+5) -5 =-5-5, 5-5, 5 6 = =-50(-8) = , 850 8, 850 6, m, m APRªABC AP PR =AB BC (0-)=040 0=40(0-) =(0-) A m 0 mp B O R m Q 40 m =t -4t- 5 t C 34

35 >0, 0->0 0<<0 PBQR Sm S==(0-) =-( -0) =-(-0) +00(0<<0) S = m 00 m 63 f()= f()= =0 f() f()=(-)(3 -+9) (-)(3 -+9)=0 -= =0 'ß3 = = 6 f()= f(-)=-4-+6-=0 f()= =0 f() f()=(+)(-)( +5+6) =(+)(-)(+)(+3) (+)(-)(+)(+3)=0 +=0 -=0 +=0 +3=0 =- = =- =-3 f()= f()=8-6+8=0 f() f()=(-)( --4) (-)( --4)=0 -=0 --4=0 = = '5 f()= f(-)=-6+3+=0 f(-)=6-4+6+=0 f() f()=(+)(+)( -3+) (+)(+)( -3+)=0 +=0 +=0-3+=0 3 '5 =- =- = 64 =t t -t-7=0, (t+8)(t-9)=0 t=-8 t=9 =-8 =9 = 'i = 3 35

36 =t t -t-=0, (t+)(t-)=0 t=-;!; t= =-;!; = ' = i = +6=0 ( +8 +6)-8 =0 ( +4) -(') =0 ( +'+4)( -'+4)=0 +'+4=0 -'+4=0 +'+4=0 =-' 'i -'+4=0 =' 'i, =-' 'i =' 'i -6 +=0 ( - +)-4 =0 ( -) -() =0 ( +-)( --)=0 +-=0 --=0 +-=0 =- ' --=0 = ', =- ' = ' -5 +5=0 ( +0 +5)-5 =0 ( +5) -(5) =0 ( +5+5)( -5+5)=0 +5+5=0-5+5=0-5 '5 +5+5=0 = 5 '5-5+5=0 = -5 '5 5 '5, = = 65 +3=t (t-3)(t+4)=8, t +t-0=0 (t+5)(t-4)=0 t=-5 t=4 t= =0-3 'ßi = t=4 +3-4=0 (-)(+4)=0 = =-4, -3 'ßi = =-4 = ( +) =0 ( +) -( +)-3=0 +=t t -t-3=0, (t+)(t-3)=0 t=- t=3 t=-, ++=0 (+) =0 =-() t=3, +-3=0 (-)(+3)=0 = =-3, =-() = =-3 {(-3)}{(-)(-)}=0 ( -3)( -3+)=0-3=t t(t+)=0 t +t-0=0, (t+)(t-0)=0 t=- t=0 t=-, -3+=0 3 'ß39i = 5 t=0, -3-0=0 (+)(-5)=0 36

37 =- =5, 3 'ß39i =- =5 = 5 {(+6)}{(+)(+4)}+5=0 ( +6)( +6+8)+5=0 +6=t t(t+8)+5=0 t +8t+5=0, (t+5)(t+3)=0 t=-5 t=-3 t=-5, +6+5=0 (+5)(+)=0 =-5 =- t=-3, +6+3=0 =-3 '6, =-5 =- =-3 '6 {(+)(+7)}{(+3)(+5)}+5=0 ( +8+7)( +8+5)+5=0 +8=t (t+7)(t+5)+5=0 t +t+0=0 (t+)(t+0)=0 t=- t=-0 t=-, +8+=0 (+)(+6)=0 =- =-6 t=-0, +8+0=0 =-4 '6, =- =-6 =-4 '6 {(-)(+)}{(-3)(+4)}+4=0 ( +-)( +-)+4=0 +=t (t-)(t-)+4=0 t -4t+48=0, (t-6)(t-8)=0 t=6 t=8 t=6, +-6=0 (-)(+3)=0 = =-3 t=8, +-8=0 - 'ß33 =, - 'ß33 = =-3 = ( +8+7)( +8+5)+5=0 +8+7=t t(t+8)+5=0, (t+3)(t+5)=0 +8+=t (t-4)(t+4)+5=0, (t-)(t+)= ;[*;+ 3 =0 { + 3 }+8{+;[!;}+7=0 {+;[!;} +8{+;[!;}+5=0 +;[!;=t t +8t+5=0, (t+3)(t+5)=0 t=-3 t=-5 t=-3,+;[!;=-3 +3+=0-3 '5 = t=-5,+;[!;=-5 +5+=0 37

38 -5 'ß = 5, -3 '5-5 'ß = 5 = ;[%;+ 3 =0 { + 3 }+5{+;[!;}-4=0 {+;[!;} +5{+;[!;}-6=0 +;[!;=t t +5t-6=0, (t+6)(t-)=0 t=-6 t= t=-6,+;[!;=-6 +6+=0 =-3 ' t=,+;[!;= '3i -+=0 = 3, '3i =-3 ' = 3-3 '5-5 'ß = = '3i =-3 ' = p+6=0 =-3-7+3p+6=0 p=7-7+6= (+3)( -3+)=0 ab -3+=0 a+b=3 p+a+b=7+3= =0-3, a, b -3+a+b=0 a+b=3 68 +a +3 ++b=0-, =-, = -a+3-+b=0 -a+b=-3 6+8a+++b=0 8a+b=-30, a=-3, b= =0 -, (+)(-)( -+3)=0 -+3= f()= +3 +(k+)+k f(-)=-+3-(k+)+k=0 f() - -3 k+ -k k - - -k -0 f()=(+)( ++k) 38

39 f()=0 ++k=0 D, ;;4;D;=-k<0 k> k> 70 f()= + +k-k- f()=++k-k-=0 f() k -k- 3 -k+ k+ 0 f()=(-)( ++k+) f()=0 ++k+=0 = ++k+=0 k=-5 ++k+=0 D, ;;4;D;=-(k+)=0 k=-, k -5+(-)= =0 a, b, c a+b+c=-, ab+bc+ca=3, abc=-4 ab+bc+ca ;å!;+;!;+;ø!;= =-;4#; abc (a+b)(b+c)(c+a) =(--c)(--a)(--b) =-(+a)(+b)(+c) =-{ +(a+b+c) +(ab+bc+ca) +abc} =-{8+(-) 4+3-4} =- c a b + + ab bc ca a +b +c = abc (a+b+c) -(ab+bc+ca) = abc (-) - 3 = 5 =;!; -4 -;4#; - ;!; =0 abc a+b+c=, ab+bc+ca=3, abc=3 b+c c+a a+b + + a b c -a -b -c = a b c ={;å!;+;!;+;ø!;}-3 ab+bc+ca = -3 abc =;3#;-3= =0 abc a+b+c=0, ab+bc+ca=3, abc= a +b +c `=(a+b+c) -(ab+bc+ca) =0-3=-6 a b +b c `+c `a =(ab+bc+ca) -(ab c+abc +a bc) =(ab+bc+ca) -abc(a+b+c) =3-0=9 a b c `=(abc) = =4 -(-6) +9-4= = =0 39

40 74 +' -' a a(+')(-')=-6 a=6 (-')+6=7-' 7-' 75 -i +i a a+(-i)+(+i)=-a a(-i)+(-i)(+i)+a(+i)=b a(-i)(+i)=5 a=, a=-5, b=9 a+b= =0 - (-)( ++)=0, -=0 = ++=0 = ++=0, = + +=( ) +( )fl + =+ + =0 ++=0 +=-,+ = ( ) ( ) = + +( ) +( ) = ` = + - -` =- (+')(+')(+' ) =(+')(+' +'+ ) =(+'){+'( +)+} =(+')(3-') +=- =+' 0 - +' 77 -=0 (-)( ++)=0 ++=0 Æ +Æ=-, Æ= + = Ǣ +- - Ǣ (-)(Ǣ ) (+Æ)- + = Ǣ (+Æ) = 5 = =- +=0, (+)( -+)=0 =- -+=0 =-, -+=0 -+=0 + =, = + ( ) +( ) 5 = ( ) -+ = - - = = - (-)(+ ) =( - +4-) = =

41 = =4( -)+ =4 (-)+=-3 fi = =- =-+ = =- fi =(-+)-(-)+(-)-(-)+ = (+)(+) (+)( +) = (-)(-) (-)( -) 4 +(+ )+ = -(+ )+ 4++ = -+ = = = =, = z=5 z=3 =, =-, z=3 --z=+4+z=3--z= ( --z= { +4+z= 9 3--z= + 3+= _+ 7+7=3 _7-_3-7=5 =-;7%; =-;7%; 7-5=3 =;7*; 79 ( -3-4z=-4 { 3+4-z= z=7 -_ -4-=8 _3+_ 7+8= _8+_ 55=55 = = 7+8= =- =, =- +6-4z=-4 z=3 =, =-, z=3 ( 5-3+z=7 { 3+4+z= z=5 -_ --= _3+ 3+7=- _3+ -36=7 =- =- =;7*;, =-;7%; ;7*;+;; 7º;;-z= z=;; 7 : =;7*;, =-;7%;, z=;; 7 : - -z z+ = = = ( -=6 { -z=3 9 z+=5 + -z=9 + =4 =7 =7 z+7=5 z=- =7 7-=6 = =7, =, z=- 80 ( +=8 { +z=3 9z+=30 ++ (++z)=90 ++z=45 - z=7 4

42 - =3 - =5 =3, =5, z=7 + +z z+ = = = ( +=7 { +z=5 9z+=6 ++ (++z)=8 ++z=9 - z= - =4 - =3 =4, =3, z= ( +3=5 { 3+5z=- 9 5z+=-3 ++ (+3+5z)=0 +3+5z=0-5z=-5 z=- - = - 3=3 = =, =, z=- (;[!;+;]!;= \ { ;]!;+;z!;= \ 9 ;z!;+;[!;=-7 ++ {;[!;+;]!;+;z!;}=-4 8 ( +-z=3 { -+3z= 9 3++z=k +_ 5+5z= z=k+, 7=k+, k=5 5 8 ( ++kz=4 { 3--z=0 9 ++z=3 + 4+(k-)z=4 + 4+z=3 - (k-)z= 0 z= k-=0 k= 83 g +=5 + =9 =5- (5-) + = =0, (-)(9-3)=0 = =: 9 : ;[!;+;]!;+;z!; =- = =3 - ;z!;=-4 z=-;4!; - ;[!;=-3 =-;3!; - ;]!;=5 =;5!; =-;3!;, =;5!;, z=-;4!; =: 9 : =-: 9 :, g =3 = =-: 9 : ª =: 9 : -3+ =0 g + =0 4

43 (-)(-)=0 = = = +() =0, =4 = = =, = 4( ) = + =0, =0 = 'ß0 = = 'ß0, = 'ß0 ( ), g = =4 g ='ß0 ='ß0 g =- =-4 g =-'ß0 =-'ß0-5+ =0 g +3+ =9 (-)(-)=0 = = = +3 + () =9 ' 5 5 =9 = 5 = ' 5 ' 5 =,= ( ) 5 5 = () +3 + =9 '3 =9 = = '3 = '3, = ( ), ' 5 = 5 { 9 = ' 5 5 ' 5 ==- ' 5 5 { 9 5 ='3 =-'3 ª = '3 ª =- '3 84 3'5 3'5 = 4 4` =-=- '5 4` 4` { 9 = 3 '5 { 9 4` - -+=0 g - ++3= _- -5-=- = =5 g =0 -_ -5+6 =0 (-)(-3)=0 = =3 = =5 '5 =;9%; = 5 3` = '5 '5 = 4, = ( ) 3` 3` = =5 '5 =; 6; = 3 4` =3 3'5 '5 = 4, = ( ) 4` 4`, '5 '5 = 4 3` =-4=- 3 '5 3` 3` { 9 = 3 '5 { 9 3` 43

44 -(-5+) -+(-5+)=0 8 -=0, (8-)=0 =0 =;8!; =0 = =;8!; =;8#;, 85 =;8!; ª =;8#; + =0 (+) -=0 g g =3 =3 +=a, =b g a -b=0 b=3 a -6=0, a =6 a= 4 a=4, b=3, +=4, =3,, t -4t+3=0 (t-)(t-3)=0 t= t=3 =, =3 =3, = a=-4, b=3, +=-4, =3,, t +4t+3=0 (t+)(t+3)=0 t=- t=-3 =-, =-3 =-3, =-, g = =3 g =- =-3 g =0 = g =3 = + ++= g ++ = g =-3 =- (+) -++= g (+) -= +=a, =b g a +a-b= a -b= b=a - a +a-(a -)= a -a=0, a(a-)=0 a=0 a= a=0 b=- a= b=0 a=0, b=-, +=0, =-,, t -=0 t = t= =, =- =-, = a=, b=0, +=, =0,, t -t=0 t(t-)=0 t=0 t= =0, = =, =0, g = =- 86 +=k =-+k + =5 +(-+k) =5 5-4k+k -5=0 D ;;4;D;=4k -5(k -5)=0 -k +5=0 k= 5 g =0 = g =- = g = =0 k 5 (-5)=

45 87 g +=a+, t =a +3 t -(a+)t+a +3=0, Dæ0 D=(a+) -4(a +3)æ0 4a-æ0 aæ: 4 : a a a -(k+4)a+5k=0 a +(k-)a-5k=0 + a -6a=0 a -3a=0, a(a-3)=0 a=0 a=3 a=0, k=0 k+0 a=3, 9-3(k+4)+5k=0 k=3 k=;#; 88 0 cm + =0 6 cm ;!;(+)(+)=;!;+6 +=4 (+) = =0 + = ,, z ++z=5 { 3++z= 9 ++z=8 - +=6 _- 5+=4, =, = =, = z=, k=;#; ;#; 9 a a +4ma-m+=0 a +ma+m+=0-3ma-3m=0 3m(a-)=0 m=0 a= m=0, +=0 a=, +4m-m+=0 m=- m=- a -4a+3=0, (a-)(a-3)=0 a= a=3 m=- a -a=0, a(a-)=0 a=0 a=, 0, 3, m=- 0, 3 m=-, =0, 3 45

46 a=, m=-, b, c +b=4, +c= b=3, c= =0 --+= (-)-(-)= (-)(-)=, -, - -æ0, -æ0 -, - g = g =3 =3 = (m-)+m+=0 a, b (a b) a+b=-m+ ab=m+ + a+b+ab= ab+a+b+=3 (a+)(b+)=3 a, b a+, b+ a b a+, b+ a+ b g a=0 b= g a=-4 b=- a=0, b=, m=-, =0 = a=-4, b=-, m=7, =-4 = =0 ( ++ )+( ++)=0 (+) +(+) =0, +=0, +=0 =-, = =-, = +(+)+ +=0 D ;;4;D;=(+) -( +)æ (-) 0 = = ++=0 (+) =0 =- =-, = =0 ( -4+4)+( -+)=0 (-) +(-) =0, -=0, -=0 =, = =, = =0 D ;;4;D;=4-( -+5)æ (-) 0 = = -4+4=0 (-) =0 = =, = 46

47 96 a<b a+c<b+c c<d b+c<b+d, a+c<b+d a-d<b-c () () a=, b=, c=4, d=8 a-c=-3, b-d=-6 a-c>b-d () () a=-, b=-, c=-4, d=- ac=8, bd= ac>bd () () a=-, b=-, c=-6, d=- ;ac;=3, ;bd;= ;ac;>;bd; () 97 <a<5, 4<b<8 4<a<0 3 <3b<4 + 6<a+3b<34 3 6<3a<5 8<b<6 - -0<3a-b<7 <a-<4 <b-<6 a- ;6!;< 45< b- 98 <4 4 <8-3< a -;3A; -;3};< + 4-;3A; -;3};<9 4-;3A;= a= ;7!; (3a+)- (a-)+4 (a+) 5 5 a>-, 4 a+ 5 a<-,æ 4 a+ a=-,0 5 5 ( a>-, 4 a+ \ { 5 a<-,æ 4 \ a+ 9 a=-, 0 a+4>a + (a-)>a -4 47

48 (a-)>(a+)(a-) <3 a-<0 (a+)(a-) < <a+ a- <3 a+=3 a= 0 aæa++ (a-)æa+ a+ a>,æ 4 a- a+ a<, 4 a- a=,0 æ a= 03 a ->+a (a -)>a+ (a+)(a-)>a+ a=-,0 >- a=,0 >3 a= <7 +<0, <-, -(+)<7 >-9 <- -9<<- +æ0, æ-, +<7 <5 æ- - <5, -9<<5 - >4 -<0, <;!;, -(-)>4 <-;#; <;!; <-;#; -æ0, æ;!; ->4 >;%; æ;!; >;%;, <-;#; >;%; + >3+5 +<0, <-, -(+)>3+5 <-;#; <- <-;#; +æ0, æ-, +>3+5 <- æ-, <-;#; < 5-;3$; < 5-;3$;<0, >: 4 :, <-{5-;3$;}<, 6<;3$;<7 ;(;<<: 4 : >: 4 : ;(;<<: 4 : 5-;3$;æ0, : 4 :, <5-;3$;<, -4<-;3$;<-3 ;4(;<<3 ;; 4 ;; ;4(;<<3 48

49 , ;4(;<<3 ;(;<<: 4 : + <7-7<+<7-9<<5 - >4 -<-4 ->4 <-;#; >;%; < 5-;3$; < -<5-;3$;<- <5-;3$;< -<5-;3$;<- -7<-;3$;<-6, 6<;3$;<7 ;(;<<;; 4 ;; <5-;3$;< -4<-;3$;<-3, 3<;3$;<4 ;4(;<<3, ;4(;<<3 ;(;<<;; 4 ;; 05 + < <, < <-, -(+)+(-)< 0 <4 <- <- - <, (+)+(-)< < - < - < æ, (+)-(-)< 0 <-,, < - + æ <-, -+(+)æ 0 æ0 <- <- - <0, --(+)æ - - <0 =- æ0, -(+)æ 0 æ,, <-3, -(-)-(+3) 5 æ- <-3-3 <, -(-)+(+3) 5 æ0-3 < 0 < æ, (-)+(+3) 5 ;3$; æ ;3$;,, 0 ;3$; 06 3-a < -<3-a< -+a -+a<3<+a 5<< +a

50 b<<4 -+a +a 5=b, =4 3 3 a=0, b=;3*; a+b=;; 3 ;; ;; 3 ;;, <- 0<<3-3 <- 0<< >0 (+)(-)> =0 (-)(-4)=0 = =4 = = -4+5 =(-) <0 =4-4+ =(-) =;!; 4 =;!; O O O = = -4+5 =4-4+ <-;!; > -- 0 (+3)(-4) æ =0 =3 ' '3 3+' (3+)(-) 0 -;3!; -4+=0 = ' -4+æ0 -' æ+' 0-6+9=(-3) > f()æg() =f() =g() -3 f()g()>0 f()>0, g()>0 f()<0, g()<0 f()>0, g()>0 0<<3 f()<0, g()<0 <- -+3 ={-;!;} +;; 4 ;;<0 -+4 =(-) +3>0 ++3 ={+;!;} +;%;>

51 4 -+9 =(-3) 0 =;#; æ0-8+9 =(-) + 0 <0, (--)(-)>0 (+)(-)<0 -<< <0 -<<0 æ0, (-)(-)>0 < > æ0 0 < >, -<< > <, -æ-(-)+ -4æ0, (+)(-)æ0 - æ < - æ, -æ(-)+ -4æ0, (-4)æ0 0 æ4 æ æ4, - æ4 -"ç -3<0 - -3<0 ( +)( -3)<0 +>0-3<0, <3-3<<3-4<0, (+)(-)<0 -<<, -( -4)<3, +3-4>0 3 (-)(+4)>0 <-4 > -<< << -4æ0, (+)(-)æ0 - æ, -4<3, -3-4<0 (+)(-4)<0 -<<4 - æ <4 << <-;!; >;3!; {+;!;}{-;3!;}>0 +;6!;-;6!;>0 a<0 a a +;6A;-;6A;<0 a +b+<0 ;6A;=b, -;6A;= a=-6, b=- a+b= <-3 >5 (+3)(-5)>0 --5>0 a +b+c<0 5

52 a<0 a a -a-5a<0 a +b+c<0 b=-a, c=-5a c +b+a<0-5a -a+a<0 5a +a-a>0 a<0 5 +-<0 (3+)(5-)<0 -;3!;<<;5!; -;3!;<<;5!; a<0 a +b+c=0-3, 5-3+5=-;aB;, -3 5=;aC; b=-a, c=-5a 4 =- -3+ =a+b - -3+>a+b +(a+3)+b-<0 -<< -<< (+)(-)<0 +-4<0 a+3=, b-=-4 a=-, b=-3 a+b= (a+) ++a 0 a+<0 a<- (a+) ++a=0 D 0 ;;4;D;=-a(a+) 0 a +a-æ0 a +a-=0 a=- ' a --' aæ-+', a --' a --' 6 a-=0, a=, 0-0 +>0 >0 a-+0, a+, a->0 a> (a-) -(a-)+=0 D<0 ;;4;D;=(a-) -(a-)<0 a -3a+<0, (a-)(a-)<0 <a<, <a<, a a< a< 7 = +(m-)+5 =+ +(m-)+5>+, +(m-)+4>0 +(m-)+4=0 D D=(m-) -6<0 m -4m-<0, (m+)(m-6)<0 -<m<6 -<m<6 5

53 8 = ++3 = +k+7 ++3< +k+7, +(k-)+4>0 +(k-)+4=0 D<0 ;;4;D;=(k-) -4<0 k -k-3<0 (k+)(k-3)<0 -<k<3 -<k<3 9-4a+a -a+<0-4a+a -a+æ0-4a+a -a+=0 D 0 ;;4;D;=4a -(a -a+) 0 3a +a- 0 (3a-)(a+) 0 - a ;3!; - a ;3!; KEY Point a +b+c>0 k a<0, b -4ac 0 a +b+cæ0 k a<0, b -4ac<0 a +b+c<0 k a>0, b -4ac 0 a +b+c 0 k a>0, b -4ac<0 0 -(k-)+k-3 0 -(k-)+k-3=0 D=0 ;;4;D;=(k-) -(k-3)=0 k -4k+4=0, (k-) =0, k= a= k= -+ 0, (-) 0, = b= a+b=3 3 <- > (+)(-)>0 f()<0 a<0 a a(+)(-)<0 f()=a(+)(-) f(3-)=a(3-+)(3--) =a(3+)(3-) f(3-)æ0, a(3+)(3-)æ0 (3+)(3-) 0 ( a<0) -;3!; ;3@; -;3!; ;3@; f()<0<- > f()æ0 - f(3-)æ ;3!; ;3@; -4>a -8-4-a +8>0 f()= -4-a +8 f()=(-) -a +4 53

54 - f()>0 =f() f()>0 -a +4>0, a -4<0 (a+)(a-)<0 -<a< - O a -, 0, =4 =4- =4- æ =k k=4+(4- ) k=-(-) +8 k 8, - O =, 8-8 =-, -8 8, =0 D æ0 D =8-4( -8-4)æ , (+)(-0) =0 D æ0 D =(-4) -(4 +6-4)æ , (+5)(-) 0-5 0, 5 +=k(k ) =k- +4 =4 +4(k-) =4 5-8k+4(k -)=0 Dæ0 ;;4;D;=(-4k) -0(k -)æ0-4k +0æ0, k 5 -'5 k '5 + '5, -'5 '5, -'5 6 [] -9[]+9<0 ([]-3)([]-3)<0 ;#;<[]<3 [] []= <3 <3 7 æ[]+[] 0 <, []=0 æ0 0 < 0 < <, []= æ+, --æ0 (+)(-)æ0 - æ <, 0 < 0 < 54

55 8 3+4<+5 <;!; -+4æ0 {-;!;} + ;; 4 ;;>0, <;!; -5+æ0 (-)(-)æ0 ;!; æ (-5)(+) 0 - ;%;, - ;!; ;%; - <4-4<-<4 -<<6 - ++<0 -->0 (+3)(-4)>0 <-3 >4, 4<<6 --7< >0 (+4)(-)>0 <-4 > (+5)(-3) 0-5 3, -5 <-4 < 3 <;!; - ;!; ;%; 4<<6-5 <-4 < >0 g -(6-a)-6a 0 (-)(-4)>0 < >4 (+a)(-6) 0 -a>6,6 -a -a<6,-a 6, 4< 6 a -a 4-4 a a a - --6<0 g -(a+)+a<0 (+)(-3)<0 -<<3 (-)(-a)<0 a<, a<<,, =0 - - a a<0 a>, <<a,, = - a 3 a>, - a<0 a> 55

56 3 +a+a -3=0 D D =a -4(a -3)æ0-3a +æ0, a a +a+a=0 D D =a -4a<0 a(a-4)<0 0<a<4, 0<a 0<a 3 >0, +>0, +>0 >0 +<+(+) > (+) < +(+) --3>0 (+)(-3)>0 <- >3,, >3 >3 33 f()= -k+k+3 f()=0-3 Dæ0, f(-3)>0, ()>-3 D=k -4(k+3)æ0 k -4k-æ0 (k+)(k-6)æ0 k - kæ6 f(-3)=9+3k+k+3>0 k>-3 =f() =;K; ;K;>-3 k>-6,, -3<k - kæ6-3<k - kæ6 34 f()= +a+3a f()=0 - Dæ0, f(-)>0, ()<- ;;;Î4;;=a -3aæ0 a(a-3)æ0 a 0 aæ3 f(-)=4-4a+3a>0 a<4 =f() =-a -a<- a>,, 3 a<4 3 a<4 35 f()= -(m-4)+m f()=0 f()<0 4-4(m-4)+m<0 m>0 m>0 36 f()= -4+k- f()=0 0 3 Dæ0, f(0)>0, f(3)>0, 0<()<3 :4;;D;=4-(k-)æ0 k 5 f(0)=k->0 k> f(3)=9-+k->0 k>4 56

57 =f() = 0<<3,, 4<k 5 4<k 5 37 f()= +(a+)+a+ =f() - f(-)>0 -(a+)+a+>0 a< f()<0 +(a+)+a+<0 a<-;3%;, a<-;3%; a<-;3%; 38 f()= +a+a-4 =f() 0 b f(-3)>0 9-3a+a-4>0-3 a a<5 f(0)<0 a-4<0 a< f()>0 4+a+a-4>0 a>0,, 0<a< 0<a< 39 III. AB =" {--(-3)} +{ -4-(-)} ='5 AB =øπ{(+'3)-} +π{-(-'3)} ='8=' '5 ' 40 AB =BC " (-3) +{ a-(-)} =" (6-) +(-a) a +4a+5=a -a+7 6a= a= 4 AB ='3 " (-a) +( -a-3) ='3 (-a) +(-a-) = a =5 a= '5 a '5+(-'5)=0 0 4 P(a, 0) AP =BP AP =BP (a-) +(0-4) ={a-(-)} +(0-3) a -a+7=a +4a+3-6a=-4 a=;3@; P{;3@;, 0} Q(0, b) AQ =BQ AQ =BQ (0-) +(b-4) ={0-(-)} +(b-3) b -8b+7=b -6b+3 -b=-4 b= Q(0, ) P{;3@;, 0}, Q(0, ) 57

58 43 P(a, b) =-+ b=-a+ P(a, -a+) A(, 3), B(, 4) AP =BP AP =BP (a-) +(-a+-3) =(a-) +(-a+-4) a -4a+4+a +a+=a -a++a +4a+4-4a=0 a=0 a=0 b= ab= ABC AB =" +(--) ='ß0 BC =" (3-) +(+) ='ß0 CA =" (-3 ) + (- ) ='ß0 AB =0, BC =0, CA =0 BC =AB +CA ABC A=90 ;!;_AB _CA =;!;_'ß0_'ß0= A A' A'(-, 9) AP =A 'P A'(-, 9) P O A(, 9) B(5, ) AP +BP =A 'P +BP æa 'B =" (5+) +(-9) =0 AP +BP P (, ) AP +BP =(+3) +(-) +(-4) +(-5) = ={-;!;} +{-;&;} +9 AP +BP =;!;, =;&; 9 P {;!;, ;&;} P{;!;, ;&;} 47 AP +BP +CP =(a+) +(b-5) +(a-3) +(b-8) +(a-5) +(b-) =3a -a+3b -30b+3 =3(a-) +3(b-5) +44 AP +BP +CP a=, b=5 44 P(, 5) m=44 a+b+m=5 5 AP +BP +CP P ABC P{ 3455, 3455 }, P(, 5) ABC P(, ) P P A =PB =PC P A =PB P A =PB (+) +(-3) =(-4) +(-5) = =7 58

59 P A =P C P A =PC (+) +(-3) =(-) +(+6) = =4, =;%;, =-;!; ABC P {;%;, -;!;} r r=p A =PB =P C ' 30 r=p A =æ {- -; %;} +{3 +;! ;} = {;%;, -;!;} ' 3ß M BC AB +AC =(AM +BM ) 9 +7 =(AM +4 ), AM =49 AM = AB P 5+ (-) (-)+ 4 {, } + + P(3, 0) AB 3 Q 3 5- (-) 3 (-)- 4 {, } 3-3- Q(7, -4) PQ (-4) { 3, 3} (0, -7) (0, -7) 5 AB b P (3, -) 6+b a+b (-5) 35=3, 35=- +b +b +b=6+3b, a-5b=--b b=6, a-b=- a=5, b=3 Q A(, -5), B(6, 5) AB 3 Q (-5) { 344, } 3-3- Q(6, 5) Q(6, 5) 5 AC =3BC AC BC =3 C AB 3 C 3 3- (-) 3 6- (-) {, } 3-3- C(, ) C(, ) 53 AB (-t)t (-t) +t (-) (-t) (-)+t 4 {, } (-t)+t (-t)+t (-3t, 5t-) -3t>0, 5t->0 ;5!;<t<;3!; (-t)t -t>0, t>0 0<t< ;5!;<t<;3!; a=;5!;, b=;3!; B(3, 6) : : a`+: : b`=5+3=8 8 3 C A(-, -) 59

60 54 AD A A(4, 9) AB AC =BD DC AB =" (-4) +( -9) =4'5 B(0, ) D C(6, 5) AC =" (6-4) +( 5-9) ='5 BD DC =AB AC =4'5'5= D BC D {, } D {4, : 3 :} + + a+b=4+: 3 :=: 3 : : 3 : 55 AB, BC, CA D, E, F ABC DEF ABC {, } (, ) 3 3 (, ) ABC A, B, C A(, ), B(, ), C(, ) A(, ) m n F m D G n O m B(, ) C(, ) E n AB, BC, CA mn(m>0, n>0) D, E, F, m +n m +n 4, 4, m+n m+n DEF DEF ABC DEF ABC DEF ABC 56 ABC a+4+0 b++5 {, }=(, ) 3 3 a+4 = a=- 3 b+7 = b=-4 3 a=-, b=-4 a=-, b=-4 57 (B D )=(A C ) D (, ) {, }={ 3, } + =-;!; =-3 + =;#; = D(-3, ) D(-3, ) 58 m +n 4 m+n m +n m +n m +n m+n m+n m+n =

61 (AC )=(BD ) +a +7 b- 5+3 {, }={, } +a b- = b=a+4 AD =DC " (+) +(-3) =" (--a) +(3-ç7) a +4a=0, a(a+4)=0 a=0 a=-4 a=0, b=4 a=-4, b=0 a<0 a=-4, b=0 a+b= =-3(+) = = 3 (+) =-;5&; +;5!; 3-(-) ;{;+;3};= =-;#; +3 =-3 =3 60 AB 5+ (-) 4+ { , } (, ) + + (, ) -3 -=-3(-) =-3+5 = ()=tan 30 = '3 3 '3 ('3, -) 3 '3 += (-'3) 3 '3 '3 = -3 = (a, 4), (-, a) 4 a-4 =4 --a a-4=-8-4a a=-;5$; 4 {-;5$;, 4} -4=4{+;5$;} =4+: 5 : =4+: 5 : 63 (, ), (3, 4) 4- = (-, ) -=3(+) =3+5 = A(-, 3), B(, ), C(a, 8) ( AB )=( BC ) = -(-) a- 6 -;3!;= a=-7-7 a- 6

62 65 ;5{;+;};= 69 a+b+c=0 a=0 =-;bc; 5, ;!;_5_= a+4=a(a>0) =0, =0 ;A; O 5 a bc<0 ;bc;<0 -;bc;>0 O, a+b+c=0 =-;ba;-;bc; -;ba;, -;bc; 8 O ;!; ;A;=8 a= =a O OAB AB AB {, } (6, -) =a (6, -) -=6a a=-;6!; -;6!; 68 k-4+3=0 ABCD {, }, (3, 3) 3k-+3=0 k=3 3 ab<0, bc<0 ;ba;<0, ;bc;<0 -;ba;>0, -;bc;>0,,, 3 O a+b+c=0 c=0 =-;ba; ab<0 ;ba;<0 -;ba;>0, 3 70,,, 3, 3 a+b+c=0 =-;ba;-;bc; -;ba;, -;bc; ab>0, bc<0 ;ba;>0, ;bc;<0 O 6

63 -;ba;<0, -;bc;>0 a+b+c= =0 -;3@; ;#; ;#; (3, -) +=;#;(-3) =;#;-: : =;#;-: : 7 a = (a-) - a = -(a-) a -a-=-, a -a=0 a(a-)=0 a=0 a= a+ -(a-) -, a=0 a = 5555 = 55 -(a-) - a = (a-) a -a-=-, a -a=0 a(a-)=0 a=0 a= = 55 a= -(a-) -, a= (a+) + {-(a-)}=0 a=-4 a (a-) a -a-+-, a -a+0, a(a-)+0 a+0, a+ 0-4 a+0, a+ 73 a-3=5-6=3 ;A;=;6#;+;3%; a=;!; 3++5=0 -b+=0 3 + (-b)=0 b=3 a+b=;!;+3=;&; ;&; AB 3=- AB 5-(-) AB AB { 3, 33 }, (, -) AB += (-) =-3 =-3 75 A BC C(, 6) D D B(8, 4) BC E =-;3!; -8 O A(3, -) AD 3 AD +=3(-3) =3-0 63

64 B AC E 6-(-) AC 33 =-7-3 BE ;7!; BE -4=;7!;(-8) =;7!;+: 7º:, =;(;, =;&; {;(;, ;&;} {;(;, ;&;} 76 ++=0 -+=0 a-=0,, - ;A;= +;); a=-, ;A;=;!;+;); a=, =-, =, (-, ) -a-=0 a=-,, a -++(-)= (k-)-(k-)-3=0 k (-+-3)+(-)k=0 k -+-3=0, -=0 =3, =6 P(3, 6) P(3, 6) 78 3+=-, -+0=0 (3++)+k(-+0)=0(k ) +0k=0 k=-; 0; k=-; 0; (3++)-; 0;(-+0)=0 4+3=0 4+3=0 =-3, =4 (-3, 4) (-3, 4), (0, 0) =-;3$; 4+3=0 79 =-;#;-;!; 3++=0 (3++)+k(-+0)=0(k ) (3+k)+(-k)++0k=0 +3-3=0 (3+k) +(-k) 3=0 k=9 k=9-7+9=0 3-+3=0 3-+3=0 80 m+-m+=0 m (-)m++=0 64

65 m (, -) ++=0 3 (-, 0), -m+=0 m=;!; (0, -), -m=0 m=0, m 0<m<;!; 8 0<m<;!; =m+ m+-=0 m (0, ) 3 B A O 5 A, B A(5, ), 5m+-=0 m=-;5!; B(, 3), m+-3=0 m=;!;, m -;5!;<m<;!; -;5!;<m<;!; A, B m -;5!; m ;!; -;5!;<m<;!; - A, B m+-;5!;, m+;!; - O ++=0 A, B AB m -;5!; m ;!; 8 +5=0, +3= =-5, = (-5, ) 3+-=0 3 (-5) = 3='ß3 " 3 + ' 3 'ß3 83 (, a) 3+-5=0 ' 0 3+a-5 33 =' 0 " 3 + a- =0, a-= 0 a= a= =0, -+3=0 (-+)+k(-+3)=0(k ) (k+)-(k+)+3k+=0 3k+ 33= " (k+) + (k+) 3k+ =" 5k +6k+ 9k +6k+=5k +6k+ 4k = k= ;!; k=;!; ;#;-+;%;= =0 65

66 k=-;!; ;!;-;!;=0 =, 3-4+5=0 = =0 = +-5+k(-)=0 (+k)+(-k)-5=0 f(k) -5 5 f(k)= 333 = 333 " (+k) + (-k) " 5k +5 f(k) " 5k +5 k k æ0 k=0 '5 5 f(k) ='5 '5 '5 86 AB AB =" (3-) + (--) =' 3 AB C(a, 4) -- -= (-) A(, ) 3- h 3+-7=0 ABC h B(3, -) C(a, 4) AB 3a+8-7 3a+ h= = " 3 + " 3 ABC 8 3a+ ;!; AB h=;!; ' 3 =8 " 3 3a+ =6, 3a+= 6 a=5 a=-: 3 : a =0, --3=0 -+=0 (0, ) --3=0 --3 ='5 '5 " +(-) =0, ++m=0 +-3=0 (0, 3) ++m=0 4' 0+3+m =4' " + 3+m =8, 3+m= 8 m=5 m=- m>0 m= P(, ) P ++3=0, --5= = " + " +(-) ++3 = = (--5) -3-8=0 3+-=0 90 (-) +(-) =3-3-8=0 3+-=0 r (-) +(+) =r (4, ) (4-) +(+) =r r =5 (-) +(+) =5 + +A+B+C=0 66

67 (0, 0), (3, ), (-, ) (0, 0) k C=0 (3, ) k 3A+B+C=-0 (-, ) k -A+B+C=-5,, A=-: 7 :,B=-: 7 :,C=0 + -: 7 :-: 7 := =0 + +A+B+C=0 (-4, 6), (-7, 3), (-, 3) (-4, 6) k -4A+6B+C=-5 (-7, 3) k -7A+3B+C=-58 (-, 3) k -A+3B+C=-0,, A=8, B=-6, C= = =0 ( ++)-+( -4+4)-4-=0 (+) +(-) =4 (-, ), = ;4!;=0 [ -+{;!;} ]-{;!;} +[ -3+{;#;} ]-{;#;} +;4!;=0 {-;!;} +{-;#;} ={;#;} {;!;, ;#;}, ;#; k=0 (+) +(-) =0-k 5 ' 0ß-k=5 0-k=5 k= (a+)+a+3a -=0 { -(a+)+(a+) }-(a+) +( +a+a )-a +3a -=0 {-(a+)} +(+a) =-a +a+3 -a +a+3>0 a -a-3<0, (a+)(a-3)<0 -<a<3 a AB 5+(-) +7 {, }=(, 4) AB ;!;AB =;!;" (-- 5) +(7 - ) =;!; 6'=3' (-) +(-4) =8 AB {, 3 }=(, -) AB ;!;AB =;!;" (5+) +(+3) =;!; ' 3=' 3 (-) +(+) =3 (-) +(-4) =8 (-) +(+) =3 67

68 (-5)(+)+(-)(-7)= =0 (-) +(-4) =8 95 =+5 (a, a+5) (a, a+5) (0, 0), (, ) " a +(a+5) =" (a-) + (a+3) a +0a+5=a +4a+0 a=-;%; {-;%;, ;%;}, {-;%;, ;%;}, (0, 0) æ {-;%;} +{;%;} 5' = 5 {+;%;} +{-;%;} =: : =+5 (a, a+5), r (-a) +(-a-5) =r (0, 0), (, ) (-a) +(-a-5) =r (-a) +(-a-5) =r a=-;%;, r =: : {+;%;} +{-;%;} =: : 96 (a, 0) (a, 0) (4, -3), (, 3) " (a-4) +3 =" (a-) + (-3) a -8a+5=a -4a+3 a=3 (3, 0), (3, 0), (4, -3) " (3-4) +3 =' 0 (-3) + =0 (-3) + =0 (a, 0), r (-a) + =r (4, -3), (, 3) (4-a) +9=r, (-a) +9=r a=3, r =0 (-3) + =0 97 PA PB =3 PA =3PB 4PA =9PB P (, ) 4{(-) + }=9{(-6) + } =0 (-0) + =36 P 6 p 6=p p 98 (3, 4) (-3) +(-4) =4 (3, 4) (-3) +(-4) =3 99 (a, b) (-a) +(-b) =a (4, 4) (4-a) +(4-b) =a 68

69 (a, b) =+ b=a+ a -a+0=0 (a-)(a-0)=0 a= a=0 a= b=4 a=0 b= (-) +(-4) =4 (-0) +(-) = (a, b) (-a) +(-b) =a (, 5), (8, -) (-a) +(5-b) =a (8-a) +(--b) =a -a-0b+b +6=0-6a+4b+b +68=0, a=5, b= a=3, b=0 (-5) +(-) =5 (-3) +(-0) = k-+8=0 (+k) +(-) =4k -7 (-k, ), = " 4k -7= 4k -7= k = k= ' -k>0 k<0, k=-' -' 30 (-, ) (-, ) r(r>0) (+r) +(-r) =r (-r, r) (-, ) (-+r) +(-r) =r r -6r+5=0, (r-)(r-5)=0 r= r=5 (-, ), (-5, 5) " (-5 +) +( 5- ) =4' 4' 303 r(r>0) (r, r) (r, r) +3=8 r+3r=8 r= (, ) (-) +(-) = k( )=0 (k+- ) (, 0) -3+3k=0 k= k= = k-4-( )=0 69

70 +(k+)-8=0 =3+4 - _3=- k+ k+=6 k= =4 + -4=0 (-) +(+) = = ( )=0-4-5=0 (0, 0), (, -) =-, =;!;, =- {;!;, -} {;!;, -} ( )=0 --= =0 (-) +(-) =4 C(, ) A A, B, AB M CM C C M B -- CM = 3 = =' " +(-) ' CM AB ACM C A =, C M =' A M =" -(') =' AB =A M =' ' 308 =+k + =5 +(+k) =5 5 +4k+k -5=0 D ;;4;D;=(k) -5(k -5)=-k +5 ;;4;D;>0 -k +5>0, (k+5)(k-5)<0-5<k<5 ;;4;D;=0 -k +5=0, k =5 k= 5 ;;4;D;<0 -k +5<0, (k+5)(k-5)>0 k<-5 k>5-5<k<5 k= 5 k<-5 k>5 (0, 0) =+k, -+k=0 d k k d= 3 = " +(-) '5 r r='5 d<r k <'5, k <5-5<k<5 '5 d=r k ='5, k =5 k= 5 '5 d>r k >'5, k >5 '5 k<-5 k>5 70

71 =0 (-) +(-3) =4 (, 3) 3-4+k=0 6-+k k-6 = 3 " 3 +(-4) 5 k-6 3 <, k-6 <0 5-0<k-6<0-4<k<6-4<k<6 30 (, )-+k=0 -+k k 4= 5 " +(-) '5 k 5, k '5 '5 -'5 k '5 k, =0 (-3) +(-4) =4 C(3, 4) -+3=0 H CH = 5=' " +(-) AC AC = CAH AH =øπac -πch =" -(') =' AB =AH =' ' A C H B 3 (3, -) -+=0 d 3++ d d= 5=3' " +(-) r (3, -) r 6 r =(3') +3 =7 r=3'3 ( r>0) 3' =0 (-) +(+) =9 C C(, -) CA ="( + ) +( - -3) ='3ß4 CB =3 ABC AB =" CA -CB AB ="( '3ß4) -3 AB ='ß5= A(-, 3) =0 (+3) +(-4) =6 (-3, 4), 4 (-3, 4) 3-4-0=0 4 (-3, 4) d = d= " 3 +(-4) d=7 7-4=3 7+4= 3 C(, -) B 3 =+ 3, 7

72 35 + =9 (, ') +' =9 +'=9 36 (, ), (, +') +'- =' - +'=9 -::!: ' -::!: (, +') ' -(+' )=-::!: ' (-) +'-'-4=0 (-) +(-) =3 (, +') (-)(-)+(+'-)(-)=3 +'-'-4= =0 (-) +(-) =9 (, ) (+', ) - =- +'- ' ' ' (+', ) -='(--') ='-7-' (-) +(-) =9 (+', ) (, ) (, +') (+'-)(-)+(-)(-)=9 ='-7-' =0 (+', ) (+')+-(+'+)-(+)-4=0 ='-7-' =0 (-) +(-) =5 (, )(3, ) - 35=;!; (3, ) -=-(-3) = , 8 ;!; 4 8=6 6 (3, ) O 4 39 =-3+5 ;3!; + =3 ;3!; =;3!; 3æ {;3!;} + =;3!; ' 0 =;3!; ' 0 30 =+b, -+b=0 7

73 (, ) 3 -+b =3 " +(-) b =3'5 b= 3'5 = 3'5 = 3'5 (-a) +(-b) =r m -b=m(-a) r" m +Ω (-) +(-) =3 -=(-) 3" + = 3'5 3 (, ) + =5 (3, -) 3 - =5 =3-5 (, ) + =5 + =5-3 +=0, ( -)( -)=0 = = (, -) (, ) --5=0 +-5=0 (3, -) m +=m(-3) m--3m-=0 (0, 0) '5 3m+ 3='5 " m +(-) 3m+ =" 5(m +) -3m- = 3m+ m +3m-=0 (m-)(m+)=0 m=;!; m=- --5=0 +-5=0 3 m =m m-= =0 (-3) +(-) = (3, ) ' 3m- 5=', 3m- =" (m +) " m + 7m -6m-=0 (m-)(7m+)=0 m= m=-;7!; -=0 +7=0 33 (, -) m +=m(-) m--m-=0 (-, ) '3 -m--m- 4 ='3 " m + -3m-3 =" 3(m +) m +3m+=0 m, m m, m m +m =

74 34 (, ) (-3, +) (a, -) (a-3, -+), (a-3, ) =-3 =(a-3)-3 a= (, ) (+, -4), -4 (-3, 4) (-3+, 4-4) (-, 0) 3-5+=0 -, +4 3(-)-5(+4)+= =0 (+) +(-) =9 -, +4 {(-)+} +{(+4)-} =9 (-) +(+) =9 36 (, ) (-, 4) -3, 3-4+=0 +3, - 3(+3)-4(-)+= =0 3+p+q=0 p=-4, q=9 p+q= (, ) (-a, +b) -a, b = -3+ +a, -b -b=(+a) -3(+a)+ = +(a-3)+a -3a+b+ = +- a-3=, a -3a+b+=- a=, b=- a+b= = -3+={-;#;} -;4!; {;#;, -;4!;}, = +-={+;!;} -;4(; {-;!;, -;4(;} {;#;, -;4!;} {-;!;, -;4(;} -, - -a=-, b=- a=, b=- a+b= =0 (+3) +(+) = =0 (-) +(-) = -a, -b {(-a)+3} +{(-b)+} = -a+3=-, -b+=- a=5, b=3 ab=5 5 (-3, -) (, ) (-3, -) a, b (, ) (-3+a, -+b)=(, ) -3+a=, -+b= a=5, b=3 ab=5 74

75 39 (, 3) P P(, -3) (, 3)= Q Q(3, ) PQ =" (3-) +(+3) =' 6 ' =-3+ =3- =-3(-)+ =3+ -=-3(-)+ =-3- ==-3+ =-;3!;+;3@; =--=-3(-)+ =-;3!;-;3@; (+3) +(--) =9 (+3) +(+) =9 (-+3) +(-) =9 (-3) +(-) =9 (-+3) +(--) =9 (-3) +(+) =9 =(+3) +(-) =9 (-) +(+3) =9 =-(-+3) +(--) =9 (+) +(-3) =9 +(-) -+6(-)+7= =0 (-) + -(-)+6+7= =0 (-) +(-) -(-)+6(-)+7= =0 = = =0 =- (-) +(-) -(-)+6(-)+7= =0 33 = -m+m -5 =(-m) -5 (m, -5) (-m, 5) (-, k) m=, k=5 m+k=7 7 = -m+m -5 -=(-) -m(-)+m -5 =- -m-m +5=-(+m) +5 (-m, 5) =0 (+3) +(-) = (-+3) +(--) = (-3) +(+) = (--3) +(+) = (+3) +(+) = (-3, -) (-3, -) (+3) +(-) = (-3, ) (3, -) (-3, -) =0 --+4=0 +-4=0 =- -+(-)-4=0 ++4=0 (+3) +(-a) = (-3, a) (-3)+a+4=0 a= 75

76 334 (a, 3), (-, b) (4, 5) a- 3+b =4, =5 a=0, b=7 ab= =- ++5 =-(-) +6 (, 6) (, 6) (a, b) (3, 6) (, 6), (3, 6) (a, b) a= =, b= =6 a+b= P(-3, 4), Q(, 8) PQ (-, 6) =a+b 6=-a+b P(-3, 4), Q(, 8) =a+b 8-4 _a=- a=- +3 a=- b=5 a-b= =0 (-) +(-4) =0 (, 4), (0, 0) =a+b (, 4), (0, 0) (, ) =a+b =a+b (, 4), (0, 0) =a+b ;$;_a=- a=-;!; a=-;!; b=;%; c=0 abc=-;!; ;%; 0= (0, -), (-, 3) {, }=(-, ) =a+b =-a+b (0, -), (-, 3) =a+b 3+ _a=- a=;!; --0 a=;!; b=;#; a+b= 339 (-) +(+3) =9 a (-a-) +(+3) =9 = (-a-) +(+3) =9 ( ) =( ) a+ =3 a+= 3 a= a=-5 a>0 a= 340 A(, 3) = A' A'(3, ) 76

77 AP =A'P AP +BP =A'P +BP æa'b =" (6-3) +(7-) =' æ0 ( ) (+) +(+3) 6 (+) +(+3) =6 ( ) + + = ( - ) 34 ' 34 =3+3 <3+3 (-a, -3) -3<-3a+3 a< =-+3 >-+3 (a, 4) A(, 3) O = B(6, 7) P O - A'(3, ) O -3-4 O 4>-4a+3 a>-;4!;, -;4!;<a< a 0, =0 (-) + =7 (-) + >7 (a, ) (a-) +>7, a -a-5>0 (a+3)(a-5)>0 a<-3 a>5 a<-3 a>5 344 f(, )=k--k+3 (-3, ), (-, ) f(-3, )f(-, ) 0 (-3k--k+3)(-k--k+3) 0 (4k-)(k-) 0 ;4!; k ;!; k ;!; ;!; [ +3 = ( ), =+3 ( ) = -3 O < + <4 3 =+3 77

78 < + [ + <4 + ->0, (-) + > (-) + = ( ), + =4 ( ) - O - (-) + = --=0, + -=0 =;!;-;!;, (-) + = = - O 3 4 (-) + = (3, 0) (3-0-)(9+0-6)=6>0 (3, 0) ( ) =0, =0, + -4=0, + -4=0 =0, =0, +(-) =4, (-) + =4 + =4 9 +(-) =4 4 (3, ) O 4 (-) + =4 (3, ) 3 (9+-4)(9+-)=-36<0 (3, ),, ( ) =0, -=0, + -9=0 =0, =, + =9 3 = (3, 3) 8-3 O 3 (3, 3) -3 + =9 3(9-3)(9+9-9)=6>0 (3, 3),, ( ) 346 =-+ =;!;- ( ) ( ) -+ 9 æ;!;- (+) + = =-- 78

79 ( ) ( ) (+) + < [ æ-- + =4, =-- ( + -4)(++)0 (0, 0) (-4) =-4<0 ( + -4)(++) , = ( ), +æ, æ-+ =-+ ( ) -+æ0, + =+ ( ) 3 O =+ = =-+ ;!; 3 =;#; =4 ( ), =+ æ+ =+ ( ) - O - + =4 ;4!; p -;!; =p- ;#; p- 348 A + = ( ), B = +k ( ) A B B k A = +k - O kæ - + = k A (-) +(-) =4 ( ), B =+k ( ) A B =+k B A O (-) +(-) =4, (, ) -+k=0 -+k = " +(-) -+k =' -+k= ' k=+' k=-' kæ+' k +' +' 79

80 , 9 + 6, æ0, æ0 3 (4, ) 6 O 9 +=6 ( +=9 ) +=k(k ) =-+k k (4, ) k k=4+=5 5 (0, 0) k k=0+0= , 0 +æ4, -æ-, + 8 ( ) +=4 - O 4 -=- (, 4) +=8 + =k(k ) 'åk (, 4)k k= +4 =0 0 +=4 k (0, 0) +-4=0 'åk -4 ='åk k=: 5 : " + : 5 : 35 0, : 5 : A, B, (700+00) P, Q 00 kg, 300 kg , A, B æ0, æ0,, ( ) =00 (0, 4) O = =k =k(k) 4+5=00, 3+0=300 (0, 4) k k= k=4800()

81 0 I. A+B=3 +-4 A-B= B= B= A=-B+(3 +-4) =-(- +3-4) =4 - (-A+B)-{B-(A-B)} =-A+B-(B-A+B) =-A-B =-(4 -)-(- +3-4) = A-3(X-B)=7A A-3X+3B=7A 3X=-6A+3B X=-A+B =-(3 -- )+( +3- ) = = (a+) =b + = + a=b= (+)c=d+e=8+4 c=4, d=8, e=4 a+b+c+d+e = = ;[!;+;]!;=4 =4 = +=4 (-) =(+) -4 =4-4 = --= ;[!;=0 -;[!;= - 3={-;[!;}3+3{-;[!;} = +3 =4 + =(+) -3(+) 4= -3 =- -+ =(+) -3 = -3 (-) =4 {+;[!;}= + ;[!;+ 3=3+=5 +;[!;='5( >0) + 3={+;[!;}3-3{+;[!;} =('5) -3 '5 =5'5-3'5 ='5 4 4 '5 + =(+)( -+ ) + =4, += -+ =4 04 ( +-4)fi (-3) a +a +a ++a +aº 8

82 aº+a ++a +a +a = (+-4)fi (-3) =(-)_= ='3 -z= - -z=-'3 + +z --z-z 05 9 (0 +)_(0 +) =(0-)(0+)(0 +)(0 +) =(0 -)(0 +)(0 +) =(0 -)(0 +) =0-06 ( )(fi -4 +-) fi (-4 )+4 fi =-48fi +4fi =-44fi fi a+b=(+' -'3 )+(-' +'3 )= ab=(+' -'3 )(-' +'3 ) ab={+(' -'3 )}{-(' -'3 )} ab=-(' -'3 ) ab=-4+'6 a +b =(a+b) -3ab(a+b) a +b = -3 (-4+'6 ) a +b =3-'6 3-'6 08 (a+b+c) =a +b +c +(ab+bc+ca) 5 =3+(ab+bc+ca) ab+bc+ca=6 (ab+bc+ca) =a b +b c +c a +(ab c+abc +a bc) =a b +b c +c a +abc(a+b+c) 6 =a b +b c +c a + (-4) 5 a b +b c +c a =76 76 =;!;{(-) +(-z) +(z-) } =;!;{('3 ) +(-'3 ) +(-) } =7-'3 ++z= +=-z, +z=-, z+=- (+)(+z)(z+) =(-z)(-)(-) = - (++z)+(+z+z)-z = =0 ++z= +=-z, +z=-, z+=- z+z +z +z + + =z(+z)+z(z+)+(+) =z(-)+z(-)+(-z) =+z+z-3z =-3 3=-7 7-' (a+b+c) =a +b +c +(ab+bc+ca) 5 =+(ab+bc+ca) ab+bc+ca= a+b+c=5 a+b=5-c, b+c=5-a, c+a=5-b (a+b)(b+c)(c+a) =(5-c)(5-a)(5-b) =5-5 (a+b+c)+5(ab+bc+ca)-abc = (-8)=8 + +z -3z =(++z)( + +z --z-z) =(++z){(++z) -3(+z+z)} 8

83 5-3z= { -3 (-5)} z=3 (++z) = + +z +(+z+z) 6 =8+(+z+z) +z+z=9 +z+z ;[!;+;]!;+;z!;=;4(; 5 =;4(; z 9 =;4(; z=4 z + +z =(++z)( + +z --z-z)+3z =6(8-9)+3 4= a +b =(a+b) -ab 5= -ab ab=- a +b =(a ) +(b ) =(a +b ) -(ab) =5 - (-) =7 a +b =(a+b) -3ab(a+b) = -3 (-) =7 afi +bfi =(a +b )(a +b )-a b (a+b) =5 7-(-) =3 +3+= ;[!;=0 +;[!;=-3 fi + 3 fi ={ + 3}{ + 3}-{+;[!;} =[{+;[!;} -][{+;[!;} -3{+;[!;}] -{+;[!;} ={(-3) -}{(-3) -3 (-3)}-(-3) =-3 a +b =7, afi +bfi =3-3, a, b, c 8 4(a+b+c)=8 a+b+c=7 4 (ab+bc+ca)=4 ab+bc+ca= a +b +c =(a+b+c) -(ab+bc+ca) =7 - =5 "a +b +c 'ß5=5 5 3 (5+3)(5 +3 )(5 +3 )(5 +3 ) =;!;(5-3)(5+3)(5 +3 )(5 +3 )(5 +3 ) =;!;(5-3 )(5 +3 )(5 +3 )(5 +3 ) =;!;(5-3 )(5 +3 )(5 +3 ) =;!;(5-3 )(5 +3 ) =;!;(5 fl -3 fl ) +3+= ;[!;=0 +;[!;=-3 + 3={+;[!;} -=(-3) -=7 + 3={+;[!;} -3{+;[!;} =(-3) -3 (-3)= ;[#; ={ + 3}-{ + 3}-3{+;[!;}+5 = (-3)+5 =-8 ;!;(5 fl -3 fl ) -8 83