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НоВыЙ13
@НоВыЙ13
July 2022
1
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Решите уравнение:
[tex] \sqrt{x^4+2x-5} = 1+x[/tex]
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ВикаВикторовна
Verified answer
√(х⁴+2х-5)= 1+х
возводим обе части в квадрат
х⁴+2х-5=1+2х+х²
х⁴-х²-6=0
х²=t
t²-t-6=0
D=1+24=25
t₁ = 1-5 / 2 = -2 - не подходит, тк х² не может быть <0
t₂ = 1+5 / 2 = 3
x² = 3
х₁ = -√3
х₂ = √3
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Answers & Comments
Verified answer
√(х⁴+2х-5)= 1+хвозводим обе части в квадрат
х⁴+2х-5=1+2х+х²
х⁴-х²-6=0
х²=t
t²-t-6=0
D=1+24=25
t₁ = 1-5 / 2 = -2 - не подходит, тк х² не может быть <0
t₂ = 1+5 / 2 = 3
x² = 3
х₁ = -√3
х₂ = √3