SOLUTION: Solve a) x^(2/3) + x^(1/3) - 2 = 0 Thanks so much in advance:)

Question 818015: Solve
a) x^(2/3) + x^(1/3) - 2 = 0
Thanks so much in advance:)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Since the exponent of the first term, 2/3, is exactly twice the exponent in the middle, 1/3, this equation is in what is known as quadratic form. Quadratic form equations have the same underlying structure as a "pure" quadratic equation and can be solved using the same techniques.

To see this more easily, it can be helpful to use a temporary variable:
Let . This makes .
Substituting these in to the equation we get:

This is obviously a quadratic equation. It will factor:

From the Zero Product Property:
q+2 = 0 or q-1 = 0
Solving these:
q = -2 or q = 1

Of course we are not interested in solutions for our made-up variable q. So we replace the q's:
or
To solve these we just cube both sides of both equations:
or

P.S. After doing several of these quadratic form equations you will no longer need the temporary variable. You will start seeing how to go directly from:

to
or
etc.
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