Question

If x=1/√3-√2 prove that

x^3 + 1/x^3 + 2(x^2+1/x^2) - 9(x+1/x)= 20

Answer 1

First : x + 1/x = 2√3

Second: x^2 + 1/x^2 = (x + 1/x)^2 - 2 *x/x = 10

x^3 + 1/x^3 = (x + 1/x)^3 - 3*(x + 1/x) = 18√3

When you replace in your equation: 18√3 + 2*10 - 9*2√3 = 20