If x = 21/3 + 22/3, show that x3 − 6x = 6
Question:

If $x=2^{1 / 3}+2^{2 / 3}$, show that $x^{3}-6 x=6$

Solution:

$x^{3}-6 x=6$

$x=2^{1 / 3}+2^{2 / 3}$

Putting cube on both the sides, we get