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

  1. Sep 26, 2012 #1

    K29

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    [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:
    [itex](\frac{\omega}{k})^{2}-(V_{1}+V_{2})\frac{\omega}{k}+\frac{1}{2}(V_{1}^{2}+V_{2}^2)=0[/itex]

    I now need to write it as:

    [itex]\frac{\omega}{k}=\frac{1}{2}(V_{1}+V_{2})\pm\frac{i}{2}(V_{1}-V_{2})[/itex]



    3. The attempt at a solution
    Substitute into the quadratic formula:

    [itex]\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/itex]

    gives:

    [itex]\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}[/itex]

    [itex]=\frac{1}{2}(V_{1}+V_{2})\pm \frac{\sqrt{(V_{1}+V_{2})^{2}-2(V_{1}^{2}+V_{2}^{2})}}{2}[/itex]

    Any ideas what to do with the terms inside the squareroot? Any help would be much appreciated
     
    Last edited: Sep 26, 2012
  2. jcsd
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