While working on some physics exercises today, I got stuck on an algebra problem. A simplified version would look something like this:

$\displaystyle x^2+x\sqrt(x^2-10)=5$

Anyone have a neat little trick for this type of problem?

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- Jan 30th 2011, 10:14 AMTwoPlusTwoDon't know how to solve this one
While working on some physics exercises today, I got stuck on an algebra problem. A simplified version would look something like this:

$\displaystyle x^2+x\sqrt(x^2-10)=5$

Anyone have a neat little trick for this type of problem? - Jan 30th 2011, 10:19 AMIthaka
- Jan 30th 2011, 10:26 AMe^(i*pi)
Subtract [tex]x^2[tex] from both sides to give $\displaystyle x\sqrt{x^2-10} = 5-x^2$

You can now square both sides but check for extraneous solutions by subbing back into your equation. Also note that $\displaystyle x^2-10 \geq 0$

off topic: Liking the sig Ithaka ;)