(x-2)^4+(x-2)^2-2=0 .Решите уравнение. Created by katusha312k. algebra-ru

(x-2)^4+(x-2)^2-2=0 .Решите уравнение...

katusha312k @katusha312k

June 2022 1 9 Report

(x-2)^4+(x-2)^2-2=0 .Решите уравнение

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Banabanana

Verified answer

(x-2)⁴+(x-2)²-2=0
Замена:
(х-2)² = t; t>0
t²+t-2=0
D=1²-4*1*(-2)=1+8=9=3²
t₁=(-1-3)/2=-2 -∅
t₂=(-1+3)/2=1
Обратная замена:
(x-2)²=1
x-2=1 или х-2=-1
х=1+2 х=-1+2
х=3 х=1

Ответ: х=1; х=3

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