if x=1/(2-3^1/2)

Question

prove that
x^3-2x^2-7x+5=3

Answer 1

start with the equation:
x^3 - 2x^2 - 7x + 2 = 0
after two tries, I found x = -2 to be a solution
so it factors to
(x+2)(x^2-4x+1) = 0
from the second ...
x = (4 ± √12)/2 = 2 ± √3

but you told me x = 1/(2-√3)
rationalizing this ...
1/(2-√3) * (2+√3)/(2+√3)
= (2+√3)/(4 - 3) = 2 + √3

which is one of the values for x I got by solving the equation.