SOLUTION: 9x^(2/3)+4x^(-2/3)=37. Find x.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 9x^(2/3)+4x^(-2/3)=37. Find x.      Log On


   

Question 829436: 9x^(2/3)+4x^(-2/3)=37. Find x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=x%5E%281%2F3%29
9x%5E%282%2F3%29%2B4x%5E%28-2%2F3%29=37
Mutliply both sides by x%5E%282%2F3%29
9x%5E%284%2F3%29%2B4=37x%5E%282%2F3%29
9x%5E%284%2F3%29-37x%5E%282%2F3%29%2B4=0
Substitute u=x%5E%282%2F3%29
9u%5E2-37u%2B4=0
%289u-1%29%28u-4%29=0
Two solutions:
9u-1=0
9u=1
u=1%2F9
x%5E%282%2F3%29=1%2F9
highlight%28x=1%2F27%29
and
u-4=0
u=4
x%5E%282%2F3%29=4
x=4%5E%283%2F2%29
highlight%28x=8%29
Now check the solution in the original equation to verify that it works.