Решите уравнение (x-2)^4-(x-2)^2-6=0

Question

Решите уравнение (x-2)^4-(x-2)^2-6=0

Answer 1

( 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 )