Решите уравнение (x-2) ^4 - (x-2) ^2-6=0

(x - 2) ^4 - (x - 2) ^2 - 6 = 0

(x - 2) ^2 = a; a > 0

a^2 - a - 6 = 0

D = 1 + 24 = 25; VD = 5

a1 = (1 + 5) : 2 = 3

a2 = (1 - 5) : 2 = - 2 (< 0)

(x - 2) ^2 = 3

x^2 - 4x + 4 - 3 = 0

x^2 - 4x + 1 = 0

D = 16 - 4 = 12; V12 = 2V3

x1 = (4 + 2V3) : 2 = 2 + V3

x2 = (4 - 2V3) : 2 = 2 - V3

Ответ (2 + V3) ; (2 - V3)