Find 3 solutions of this expression I Math Olympiad Problem

In this algebraic problem, you have to find 3 solutions for 'x' .

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[outlaw]

My solution

(x-1)^3 = 1

Thus, x-1 is a cube root of 1. It can be either equal to 1 or w or w^2 (here w is omega)

Putting these values
1) x-1=1
x=2

2) x-1 = w = (-1+i√3)/2
x= (1+i√3)/2

3) x-1 = w^2 = (-1-i√3)/2
x=(1-i√3)/2

[Birol]

Our solution set is: L= {2, (1+i√3)/2, (1-i√3)/2}