SOLUTION: Solve for x: 2x^(-2/3)- 5x^(-1/3) - 3 = 0 Any help is greatly appreciated!

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Solve for x: 2x^(-2/3)- 5x^(-1/3) - 3 = 0 Any help is greatly appreciated!      Log On


   

Question 842630: Solve for x: 2x^(-2/3)- 5x^(-1/3) - 3 = 0
Any help is greatly appreciated!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, Previously Posted

2x%5E%28-2%2F3%29+-+5x%5E%28-1%2F3%29+-+3+=+0

The Idea is to Let n = x%5E%28-1%2F3%29   

  2n^2 - 5n - 3 = 0

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

  (2n+1)= 0, n = -1/2,  x+=+1%2F%28-1%2F8%29+=+-8

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

n = 1%2Fx%5E%281%2F3%29 , n^3 = 1/x (Cubing both sides)    0r x = 1/n^3