if x=2^1/3 + 2^2/3 show that x^3-6x =6

Answer 1

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