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April 17th, 2014, 01:03 PM   #1
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solve abs(x^2-abs(x))=2

Last edited by mared; April 17th, 2014 at 01:05 PM.
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April 17th, 2014, 05:29 PM   #2
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To remove the outer absolute value, solve $x^2-|x|=\pm 2$. To remove the inner absolute value, consider two cases: (1) $x<0$ and $|x|=-x$ or (2) $x\ge0$ and $|x|=x$.
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April 18th, 2014, 05:38 PM   #3
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Remember that $|x|^2 =x^2$

The first step is then to square the equation, noting that no solutions are added.

Last edited by v8archie; April 18th, 2014 at 06:37 PM.
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