finding real solutions...?

Question

3x^1/3 +2x^2/3 =5


heh i haven't done these in a while... where do i start? please help me out with the steps as to how to find the solutios for it... thank you!

Answer 1

To see it as a quadratic, let x^1/3 = u. Then you have
3u + 2u² = 5
2u² + 3u - 5 = 0
(2u + 5)(u - 1) = 0
u = -5/2 or u = 1
x^1/3 = -5/2 or x^1/3 = 1
x = -125/8 or x = 1