Question

X=3-2 root 2 find x^3+1/x^3

Answer 1

x = 3 - 2√2 
1/x =  [3 + 2√2 ] / [9 - 8]   = 3 + 2 √2 after rationalization.

x + 1/x = 6

(x+1/x)³ = 6³ = x³ + 1/x³ + 3 *x * 1/x ( x + 1/x)

so  x³ + 1/x³ = 216 - 3 * 6 = 198