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What is the best way to solve this equation :

$\sqrt{9x-y^{2}}-\sqrt{y+3}-\sqrt{9x^{2}+y}=0$

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    There are solutions, but as [Wolfram Alpha](http://www.wolframalpha.com/input/?i=sqrt%289x-y%5E2%29+%3D+sqrt%28y%2B3%29+%2B+sqrt%289x%5E2+%2B+y%29) shows, I wouldn't think any simple method would yield them.2012-08-22

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You have an equation like $a-b-c=0$, which is equivalent to $a-b=c$. Then you take the squares $(a-b)^2=c^2$ and go on.

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    Yes, but be careful because of extraneous roots (the squaring operation is not one-to-one). So any solutions you get must be checked by plugging them in to the original equation. In this particular case it looks to me like there are no real solutions.2012-08-22