if x=2^1/3 + 2^2/3 show that x^3-6x =6
just plug and chug:
x = ∛2+∛4
x^3 = (∛2+∛4)^3
= 2 + 3∛16 + 3∛32 + 4
= 2 + 6∛2 + 6∛4 + 4
= 6 + 6∛2 + 6∛4
now subtract 6x to get 6
x = ∛2+∛4
x^3 = (∛2+∛4)^3
= 2 + 3∛16 + 3∛32 + 4
= 2 + 6∛2 + 6∛4 + 4
= 6 + 6∛2 + 6∛4
now subtract 6x to get 6