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Math Help - Simultaneous Equations

  1. #1
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    Simultaneous Equations

    \cosh x + \cosh y = 4
    \sinh x + \sinh y = 2

    I didn't get very far after writing it out in exponential form.
    Anyone willing to give me a pointer?
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  2. #2
    Super Member wingless's Avatar
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    \cosh x + \cosh y = 4
    \sinh x + \sinh y = 2

    We know that \cosh x + \sinh x = e^x and \cosh x - \sinh x = e^{-x}.

    Then,
    \cosh x + \cosh y = 4
    \sinh x + \sinh y = 2

    Add:
    \cosh x + \cosh y + \sinh x + \sinh y = 6
    e^x + e^y = 6

    Subtract:
    \cosh x + \cosh y - \sinh x - \sinh y = 2
    e^{-x} + e^{-y} = 2

    So we have,
    e^x + e^y = 6

    e^{-x} + e^{-y} = 2

    \frac{1}{e^x} + \frac{1}{e^y} = 2

    \frac{e^x + e^y}{e^x e^y} = 2

    \frac{6}{e^x e^y} = 2

    e^x e^y = 3

    e^y = \frac{3}{e^x}

    e^x + e^y = 6

    e^x + \frac{3}{e^x} = 6

    Let a = e^x

    a + \frac{3}{a} = 6

    a^2 + 3 = 6a

    a^2 - 6a + 3 = 0

    a = \frac{6 \mp \sqrt{24}}{2} = 3 \mp \sqrt{6}

    x = \ln (3 \mp \sqrt{6})

    I think you can find ys for the xs we found
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