SOLUTION: Need to find all real solutions for problems with fractional exponents and do not understand. Problem I have is x2/3 - x1/3 -20 = 0 Do not even know where to begin with the fracti

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Need to find all real solutions for problems with fractional exponents and do not understand. Problem I have is x2/3 - x1/3 -20 = 0 Do not even know where to begin with the fracti      Log On


   

Question 230601: Need to find all real solutions for problems with fractional exponents and do not understand. Problem I have is x2/3 - x1/3 -20 = 0
Do not even know where to begin with the fractions, can you help?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x2/3 - x1/3 -20 = 0
----------
I think you mean:
x%5E%282%2F3%29+=+x%5E%281%2F3%29+-+20+=+0
This is a quadratic in x^(1/3).
x%5E%282%2F3%29+=+%28x%5E%281%2F3%29%29%5E2
Solve it as a quadratic to find x^(1/3).
It can be factored:
= %28x%5E%281%2F3%29+-+5%29%2A%28x%5E%281%2F3%29+%2B+4%29
x^(1/3) = 5, -4
x = 125, -64