SOLUTION: I'm having difficulty solving this question: Solve for x: 2x^(-2/3) - 5x^(-1/3) - 3 = 0 Here is where I'm stuck: 2/x^(2/3) - 5/(x^(1/3) = 3 What do I do from here?

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: I'm having difficulty solving this question: Solve for x: 2x^(-2/3) - 5x^(-1/3) - 3 = 0 Here is where I'm stuck: 2/x^(2/3) - 5/(x^(1/3) = 3 What do I do from here?      Log On

 

Hi,



The Idea is to Let n =    

  2n^2 - 5n - 3 = 0

(2n+1)(n-3)= 0

  (2n+1)= 0, n = -1/2,  

0r (n-3)= 0, n = 3 ,    x = 1/27 

n =  , n^3 = 1/x (Cubing both sides)    0r x = 1/n^3