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semenpolukhin
@semenpolukhin
July 2022
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РЕШИТЕ УРАВНЕНИЕ (x+3)^4+2(x+3)^2-8=0, пожалуйста полное решение:3
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nKrynka
Решение
(x+3)^4+2(x+3)^2-8=0
(x + 3)
² = t, t ≥ 0
t
⁴ + 2t - 8 = 0
t₁ = - 4 не удовлетворяет условию t ≥ 0
t₂ = 2
(x + 3)² = 2
1) x + 3 = - √2
x₁ = - 3 - √2
2) x + 3 = √2
x₂ = - 3 + √2
Ответ: x₁ = - 3 - √2;
x₂ = - 3 + √2
3 votes
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Answers & Comments
(x+3)^4+2(x+3)^2-8=0
(x + 3)² = t, t ≥ 0
t⁴ + 2t - 8 = 0
t₁ = - 4 не удовлетворяет условию t ≥ 0
t₂ = 2
(x + 3)² = 2
1) x + 3 = - √2
x₁ = - 3 - √2
2) x + 3 = √2
x₂ = - 3 + √2
Ответ: x₁ = - 3 - √2; x₂ = - 3 + √2