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Math Help - Help me resolve this...

  1. #1
    Newbie
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    Feb 2012
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    Unhappy Help me resolve this...

    I have this equation that I would like to simplify.





    I suspect that the equation is actually independent of r.

    But I am having a hard time simplifying so that it is only expressed in terms of c and d.

    Can you guys help me out?
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  2. #2
    MHF Contributor
    Joined
    Dec 2007
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    Ottawa, Canada
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    Re: Help me resolve this...

    That's NOT an equation, so nothing can be done...

    Let's make it equal to K. Here's the quadratic you'd get:

    r^2[c^2(16d^2 - 16K - 4c^2)] + r[c^3(16d^2 - 16K - 4c^2)]
    + c^2(8c^2 d^2 - c^4 - 4Kc^2 - 16d^4 - 16Kd^2) = 0

    You could let U = 16d^2 - 16K - 4c^2, so getting a more manageable:

    r^2(Uc^2) + r(Uc^3) + c^2(8c^2 d^2 - c^4 - 4Kc^2 - 16d^4 - 16Kd^2) = 0

    I guess you could now let V = 8c^2 d^2 - c^4 - 4Kc^2 - 16d^4 - 16Kd^2, to get:

    r^2(Uc^2) + r(Uc^3) + Vc^2 = 0

    r = [-Uc^3 +- SQRT(U^2 c^6 - 4UVc^4)] / (2Uc^2)

    WHERE d'heck did you ever get that anyway?
    Last edited by Wilmer; March 1st 2012 at 09:12 PM.
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