(x^2-5x)^2+10(x^2-5x+1)+14=0 (Уравнение с водящимся уравнениями). Created by sashashuman20. algebra-ru

(x^2-5x)^2+10(x^2-5x+1)+14=0 (Уравнение с водящимся уравнениями)...

sashashuman20 @sashashuman20

August 2022 1 5 Report

(x^2-5x)^2+10(x^2-5x+1)+14=0 (Уравнение с водящимся уравнениями)

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sangers1959

Verified answer

(x²-5x)²+10*(x²-5x+1)+14=0
(x²-5x)²+10*(x²-5)+10+14=0
(x²-5x)+10*(x²-5)+24=0
x²-5x=t ⇒
t²+10t+24=0 D=4
t₁=-6 x²-5x=-6 x²-5x+6=0 D=1 x₁=3 x₂=2
t₂=-4 x²-5=-4 x²-5x+4=0 D=9 x₃=4 x₄=1.

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