Online Course Discussion Forum

Math Challenge Three 3.26 Algebra

 
 
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Math Challenge Three 3.26 Algebra
by Xinxin Fang - Saturday, September 26, 2020, 8:10 PM
 
Can't find a way to eliminate the square roots.
 
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Re: Math Challenge Three 3.26 Algebra
by Dr. Kevin Wang - Sunday, September 27, 2020, 12:22 AM
 

This is the question:

Find the real roots of \[ x + \sqrt{x+\frac{1}{2} + \sqrt{x + \frac{1}{4}}}=4. \]

Here is a hint: use the following change of variables: $y=\sqrt{x + \dfrac{1}{4}}$. Then $x=y^2 - \dfrac{1}{4}$.