Question

find all real and imaginary solutions

x^(2/3)-2=x^(1/3)

Answer 1

let x^(1/3) = y, then your equation becomes

y^2 - 2 = y
y^2 - y - 2 = 0
(y-2)(y+1) = 0
y = 2 or y = -1

then

x^(1/3) = 2
x = 8

or

x^(1/3) = -1
x = -1