Решите уравнение. 2 * (x^2 + 1/x^2) - (x + 1/x) = 6

Замена: x+1/x = t

(x+1/x) ^2 = x^2+2+1/x^2 = t^2

получим:

2 * (t^2 - 2) - t = 6

2t^2 - t - 10 = 0

D = 1+4*2*10 = 9^2

(t) 1; 2 = (1+-9) / 4

x+1/x = 2.5 x+1/x = - 2

x^2 - 2.5x + 1 = 0 x^2 + 2x + 1 = 0

2x^2 - 5x + 2 = 0 (x+1) ^2 = 0

D=25-4*2*2 = 3^2 x = - 1

(x) 1; 2 = (5+-3) / 4

x = 2

x = 0.5