Answer:
x = -1, 7, 3 + i, 3 - i.
Step-by-step explanation:
(x^2-6x+9)^2-15(x^2-6x+10)=1
(x^2 - 6x + 9)^2 - 15(x^2 - 6x + 9) - 15*1 = 1
(x^2 - 6x + 9)^2 - 15(x^2 - 6x + 9) - 16 = 0
Let Z = x^2 - 6x + 9, then we have:
Z^2 - 15Z - 16 = 0
(Z - 16)(Z + 1) = 0
Z = 16 or Z = -1
so x^2 - 6x + 9 = -1 or x^2 - 6x + 9 = 16
x^2 - 6x + 9 = -1
---> x^2 - 6x + 10 = 0
Using the Quadratic Formula:
---> x = [6 +/- √((-6)^2 - 4* 1* 10) / 2
---> x = 6/2 +/- √-4/2
---> x = 3 + i , 3 - i.
x^2 - 6x + 9 = 16
---> x^2 - 6x - 7 = 0
---> (x - 7)(x + 1) = 0
---> x = 7, -1.