Expert: Paul Klarreich - 3/26/2009

Question
I don't remember how to solve this problem. I know how to get rid of the radical. ³√(4x²+3)=³√(x²+10x)

Answer
Questioner:   Tom
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Algebra 3rd root radical
Question:  I don't remember how to solve this problem. I know how to get rid of the radical. ³√(4x²+3)=³√(x²+10x)
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OK, if you know that, what don't you know?

Perhaps you meant : I don't know how....

So you just cube both sides and get:

4x^2 + 3 = x^2 + 10x

which is just a quadratic equation.  [Factors nicely, too.]

3x^2 - 10x + 3 = 0
(3x - 1)(x - 3) = 0
x = 1/3,  x = 3

etc.