Log0,5 (x^6-6x^4+12x^2-8=-3 решите логарифметическое уравнение

Log0,5 (x^6 - 6x^4 + 12x^2 - 8) = - 3

x^6 - 6x^4 + 12x^2 - 8 = (1/2) ^-3

x^6 - 6x^4 + 12x^2 - 8 = 8

x^6 - 6x^4 + 12x^2 - 16 = 0

Замена переменных

t = x^2

t^3 - 6^2t + 12t - 16 = 0

(t^3 - 3*2*t^2 + 3*2^2*t + (-2) ^3)) - 8 = 0

(t - 2) ^3 - 8 = 0

(t - 2) ^3 - 2^3 = 0

(t - 4) (t^2 - 2t + 4) = 0

t - 4 = 0 t^2 - 2t + 4 = 0

t = 4 D = (-2) ^2 - 4*4 = 4 - 16 = - 12

Находим значения х

x^2 = 4

x1 = 2

x2 = - 2