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Thread: Simultaneous non-linear equations.

  1. #1
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    Simultaneous non-linear equations.

    {5xy(x + y) = -160
    {x + 5xy +y = -12
    ???
    Last edited by mr fantastic; Sep 19th 2011 at 07:28 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: No idea

    What do you have to do? Solve the system? ...
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  3. #3
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    Re: No idea

    Yes
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: No idea

    The first thing I noticed is that you recognize two equal parts in both equations, the $\displaystyle 5xy$ part and $\displaystyle x^2+y^2$

    So you can 'simplify' the system by saying, let $\displaystyle x^2+y^2=a$ and $\displaystyle 5xy=b$ therefore you get the two simultaneous equations:
    $\displaystyle b\cdot a=-160$ (1)
    $\displaystyle a+b=-12$ (2)

    Solve this system and afterwards do the back-substitution.
    Last edited by Siron; Sep 19th 2011 at 11:23 AM.
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  5. #5
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    Re: No idea

    Thank you very much
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: No idea

    You're welcome!

    I'll give you a part of the solution,
    Solving the system by reforming (1) to $\displaystyle b$ and substituting this in (2):
    $\displaystyle a-\frac{160}{a}=-12$
    $\displaystyle \Leftrightarrow a^2-160=-12a$
    $\displaystyle \Leftrightarrow a^2+12a-160=0$
    Two solutions: $\displaystyle a=8$ or $\displaystyle a=-20$
    But we have to reject $\displaystyle a=-20$ because $\displaystyle a=x^2+y^2$ is always >0.
    If $\displaystyle a=8$ then $\displaystyle b=-20$

    So now you can do the back-substitution and solve it.
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