x^3 - 2x + 1 = 0

It holds when x =1/.Is this a guess? If there is, I will say X 3-2x+1= 0 = (X-1) (X 2+X-1), if not, I will use cubic equation to find the root formula.

Divided by the polynomial (x3-2x+1)/(x-1) = x2+x-1.

The solution of x 2+x- 1 = 0 gives x = (- 1+√5)/2, (-1-√5)/2.

So three: 1, (-1+√5)/2, (-1-√5)/2.