# Don't know how to solve this one

• Jan 30th 2011, 10:14 AM
TwoPlusTwo
Don'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 AM
Ithaka
Quote:

Originally Posted by TwoPlusTwo
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?

Write it as:

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

And then square both sides.
• Jan 30th 2011, 10:26 AM
e^(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 ;)