find the real solutions of the equation

Question

6x^(2/3) -35x^(1/3) -6=0

Answer 1

6x^2/3 - 35x^1/3 - 6 = 0

 

6(x^1/3)² - 35(x^1/3) - 6 = 0

 

Let u = x^1/3

 

So, in terms of u, the equation becomes:  6u² - 35u - 6 = 0

 

                                                          (6u + 1)(u - 6) = 0

 

                                                            u = -1/6 or u = 6

 

x^1/3 = -1/6 or x^1/3 = 6

 

x = (-1/6)³ or 6³

 

x = -1/216 or 216