Question

7(x+1/x)-2(x^2+1/x^2)=9 пожалуйста

Answer 1

(x + 1/x) = t

(x + 1/x)² = x² + 1/x² + 2 = t²

x² + 1/x² = t² - 2

7t - 2t² + 4 = 9
2t² - 7t + 5 = 0
D = 49 - 40 = 9
t1 = (7-3)/4 = 1
t2 = (7+3)/4 = 2,5

x + 1/x = 1
x² - x + 1 = 0
D = 1 - 4 < 0 - не имеет решений

x + 1/x = 2,5
x² - 2,5x + 1 = 0
D = 6,25 - 4 = 2,25 = (1,5)²

x1 = (2,5 - 1,5)/2 = 0,5
x2 = (2,5 + 1,5)/2 = 2

Ответ: 0,5 и 2