Решите, пожалуйста, уравнение[tex](2x-1)^{4} -x^2=0[/tex]. Created by ooohh. algebra-ru

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ooohh @ooohh

July 2022 1 5 Report

Решите, пожалуйста, уравнение
[tex](2x-1)^{4} -x^2=0[/tex]

Answers & Comments

Artem112

Verified answer

$(2x-1)^{4} -x^2=0
\\\
((2x-1)^2-x)((2x-1)^2+x)=0
\\\
(4x^2-4x+1-x)(4x^2-4x+1+x)=0
\\\
(4x^2-5x+1)(4x^2-3x+1)=0
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4x^2-5x+1=0
\\\
D=25-16=9
\\\
x_1=1
\\\
x_2= 0.25
\\\
4x^2-3x+1=0
\\\
D=9-16$
Ответ: 1 и 0,25

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