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1CheshireCat1
@1CheshireCat1
July 2022
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номер 6.144 и 6.147 из сборника Сканави
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sedinalana
6/(x²+3x+2)+8/(x²+3x-4)=1
(x+1)(x+2)(x-1)(x+4)≠0⇒x≠-1,x≠-2;x≠1,x≠-4
x²+3x+2=a⇒x²+3x-4=a-6
6/a+8/(a-6)=1
6*(a-6)+8*a=a(a-6)
a²-6a-6a+36-8a=0
a²-20a+36=0
a1+a2=20 U a1*a2=36
a1=2⇒x²+3x+2=2
x²+3x=0
x(x+3)=0
x=0 U x=-3
a2=18⇒x²+3x+2=18
x²+3x-16=0
x1+x2=-3 U x1*x2=-16
x1=-8 U x2=2
Ответ x={-8;-3;0;2}
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Answers & Comments
(x+1)(x+2)(x-1)(x+4)≠0⇒x≠-1,x≠-2;x≠1,x≠-4
x²+3x+2=a⇒x²+3x-4=a-6
6/a+8/(a-6)=1
6*(a-6)+8*a=a(a-6)
a²-6a-6a+36-8a=0
a²-20a+36=0
a1+a2=20 U a1*a2=36
a1=2⇒x²+3x+2=2
x²+3x=0
x(x+3)=0
x=0 U x=-3
a2=18⇒x²+3x+2=18
x²+3x-16=0
x1+x2=-3 U x1*x2=-16
x1=-8 U x2=2
Ответ x={-8;-3;0;2}