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

Question

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

Answer 1

(x^1/3)² - 3(x^1/3) + 2 = 0

 

Let u = x^1/3   Then the equation becomes u² - 3u + 2 = 0

 

                                                                (u-2)(u-1) = 0

 

                                                                      u = 2 or u = 1

 

Since u = x^1/3, we have x^1/3 = 2 or x^1/3 = 1

 

                               So, x = 2³ or 1³

 

                                     x = 8 or x = 1