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olegfomenko
@olegfomenko
July 2022
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|x|^4 -2x^2 + 1 = 0 Решите Пожалуйста уравнение
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oganesbagoyan
Verified answer
Решите уравнение
|x|^4 -2x^2 + 1 = 0
---.---.---.---.---.---.---.---.---.---.
---.---.---.---.---.---.---.---.---.---
|x|⁴ -2x²
+ 1 = 0 ;
(|x|²)² -2|x|²
+ 1 = 0 ;
(|x|² -1)² =0 ;
|x|² -1 =0 ; * * * или ( |x| +1)*(|x| -1) =0 ⇒|x| +1 =0 или |x| -1 =0 * * *
|x|² =1;
|x| =± 1 , но |x| ≠ -1 * * *
|x|
≥0 * * *
|x| = 1 ;
x =± 1
ответ : -1 ; 1
.
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Answers & Comments
Verified answer
Решите уравнение |x|^4 -2x^2 + 1 = 0---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---
|x|⁴ -2x² + 1 = 0 ;
(|x|²)² -2|x|² + 1 = 0 ;
(|x|² -1)² =0 ;
|x|² -1 =0 ; * * * или ( |x| +1)*(|x| -1) =0 ⇒|x| +1 =0 или |x| -1 =0 * * *
|x|² =1;
|x| =± 1 , но |x| ≠ -1 * * * |x| ≥0 * * *
|x| = 1 ;
x =± 1
ответ : -1 ; 1 .