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