Question

Даю 25б СРОЧНО Решить уравнение с помощью t

Answer 1

x² + 16/x² - x - 4/x = 12

(x² + 16/x²) - (x + 4/x) - 12 = 0

x + 4/x = t

(x + 4/x)² = t²

x² + 16/x² + 2*x*4/x = t²

x² + 16/x² = t² - 8

t² - 8 - t - 12 = 0

t² - t - 20 = 0

D = 1 + 80 = 81

t12= (1 +- 9)/2 = 5   -4

1/ t = -4

x + 4/x = -4

x² + 4x + 4 = 0

(x + 2)² = 0

x = -2

2. t = 5

x + 4/x = 5

x² - 5x + 4 = 0

x=1

x=4

ответ  -2  1 4