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ireena
@ireena
July 2022
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уравнение в приложенном рис
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ShirokovP
Verified answer
(x + 2)⁴ + 2x² + 8x - 16 = 0;
(x + 2)⁴ + 2(x² + 4x - 8) = 0;
(x + 2)⁴ + 2(x² + 4x + 4 - 12) = 0;
(x + 2)⁴ + 2((x+2)² - 12) = 0;
(x + 2)⁴ + 2(x + 2)² - 24 = 0;
Пусть t = (x + 2)², тогда t² + 2t - 24 = 0
D = ( - 2)² - 4*( - 24) = 4 + 96 = 100
t₁ = ( - 2 + 10) / 2 = 4
t₂ = ( - 2 - 10) / 2 = - 6
Обратная замена
t₁ = 4;
(x + 2)² = 4;
x + 2 = ±√4;
x₁ = -2 + 2 = 0;
x₂ = -2 - 2 = - 4.
Ответ:
- 4; 0
2 votes
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Answers & Comments
Verified answer
(x + 2)⁴ + 2x² + 8x - 16 = 0;(x + 2)⁴ + 2(x² + 4x - 8) = 0;
(x + 2)⁴ + 2(x² + 4x + 4 - 12) = 0;
(x + 2)⁴ + 2((x+2)² - 12) = 0;
(x + 2)⁴ + 2(x + 2)² - 24 = 0;
Пусть t = (x + 2)², тогда t² + 2t - 24 = 0
D = ( - 2)² - 4*( - 24) = 4 + 96 = 100
t₁ = ( - 2 + 10) / 2 = 4
t₂ = ( - 2 - 10) / 2 = - 6
Обратная замена
t₁ = 4;
(x + 2)² = 4;
x + 2 = ±√4;
x₁ = -2 + 2 = 0;
x₂ = -2 - 2 = - 4.
Ответ:
- 4; 0