(X2+8x)(x2+8x-6)=280. Created by Olchik27. algebra-ru

(X2+8x)(x2+8x-6)=280...

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Пусть t = x² + 8x, тогда получаем:
t * (t - 6) = 280
t² - 6t - 280 = 0
D = 36 + 4*280 = 1156 = 34^2
t₁ = (6 + 34)/2 = 40/2 = 20
t₂ = (6 - 34)/2 = -28/2 = -14

Делаем обратную подстановку:
1) x² + 8x = 20
x² + 8x - 20 = 0
D = 64 + 80 = 144 = 12^2
x₁ = ( - 8 + 12)/2 = 4/2 = 2
x₂ = ( - 8 - 12)/2 = - 20/2 = -10

2) x² + 8x = -14
x² + 8x + 14 = 0
D = 64 - 4*14 = 8
√D = 2√2
x₃ = ( - 8 - 2√2)/2 = - 4 - √2
x₄ = ( - 8 + 2√2)/2 = - 4 + √2

Ответ:
2; - 10; - 4 - √2; - 4 + √2

3 votes Thanks 4

gfirsov0071 (x² + 8x)(x² + 8x - 6) = 280

t = x² + 8x

t(t - 6) = 280

t² - 6t - 280 = 0

t = 20 и t = -14 по теореме Виета.

1) х² + 8х - 20 = 0

х = -10 и х = 2 по теореме Виета

2) х² + 8х + 14 = 0

х = -4 ± √(16 - 14) = -4 ± √2

Ответ: -10; 2; -4 ± √2

0 votes Thanks 2

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