# Homework Help: Need help with algebra at the end of fluids/waves problem

1. Sep 26, 2012

### K29

[SOLVED]Need help with algebra at the end of fluids/waves problem

EDIT: Ignore this post. Stupid. Solution was obvious. Unfortunately not obvious soon enough :/

1. The problem statement, all variables and given/known data
The fluids problem is not really important.
I have solved the wave problem to get the following dispersion equation:
$(\frac{\omega}{k})^{2}-(V_{1}+V_{2})\frac{\omega}{k}+\frac{1}{2}(V_{1}^{2}+V_{2}^2)=0$

I now need to write it as:

$\frac{\omega}{k}=\frac{1}{2}(V_{1}+V_{2})\pm\frac{i}{2}(V_{1}-V_{2})$

3. The attempt at a solution

$\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

gives:

$\frac{\omega}{k}=\frac{(V_{1}+V_{2})\pm \sqrt{(-(V_{1}+V_{2}))^{2}-4(\frac{1}{2}(V_{1}^{2}+V_{2}^{2}))}}{2}$

$=\frac{1}{2}(V_{1}+V_{2})\pm \frac{\sqrt{(V_{1}+V_{2})^{2}-2(V_{1}^{2}+V_{2}^{2})}}{2}$

Any ideas what to do with the terms inside the squareroot? Any help would be much appreciated

Last edited: Sep 26, 2012