найти сумму корней 1/(x^2-3x-3)+5/(x^2,-3x+1)=2. Created by shakhggggggg. algebra-ru

(x^2,-3x+1)=2...

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July 2022 1 14 Report

найти сумму корней 1/(x^2-3x-3)+5/(x^2,-3x+1)=2

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oganesbagoyan

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task/24841586
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найти сумму корней 1/(x^2-3x-3)+5/(x^2,-3x+1)=2
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1/(x²-3x-3)+5/(x²-3x+1) =2 ;
замена x²-3x -1 = t
1/(t-2) +5/(t+2) =2 ;
(t+2 +5t -10) =2(t² -4) ;
2(3t -4) =2(t² -4) ;
t² -3t =0 ;
t(t-3) =0 ;
t₁ = 0 ⇒ x²-3x -1 =0 || D =3² -4*1*(-1) =13 >0 || ⇒ x₁ +x₂ = 3.
t ₂ = 3⇒ x²-3x -1 =3⇔x²-3x -4 =0 ⇒ x₃+x₄=3 * * * x₃= -1 , x₄ = 4 * * *

ответ : x₁ +x₂+x₃+x₄=3+ 3 = 6 .

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