Results 1 to 2 of 2

Thread: Simultaneous Equations

  1. #1
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591

    Simultaneous Equations

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

    I didn't get very far after writing it out in exponential form.
    Anyone willing to give me a pointer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    $\displaystyle \cosh x + \cosh y = 4$
    $\displaystyle \sinh x + \sinh y = 2$

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

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

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

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

    So we have,
    $\displaystyle e^x + e^y = 6$

    $\displaystyle e^{-x} + e^{-y} = 2$

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

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

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

    $\displaystyle e^x e^y = 3$

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

    $\displaystyle e^x + e^y = 6$

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

    Let $\displaystyle a = e^x$

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

    $\displaystyle a^2 + 3 = 6a$

    $\displaystyle a^2 - 6a + 3 = 0$

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

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

    I think you can find $\displaystyle y$s for the $\displaystyle x$s we found
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simultaneous Equations 4 variables, 4 equations
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Dec 7th 2011, 04:06 PM
  2. Simultaneous equations.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 16th 2011, 05:09 PM
  3. Simultaneous log equations
    Posted in the Algebra Forum
    Replies: 6
    Last Post: Mar 28th 2010, 06:52 AM
  4. Replies: 3
    Last Post: Feb 27th 2009, 07:05 PM
  5. simultaneous equations
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Feb 5th 2009, 09:20 PM

Search Tags


/mathhelpforum @mathhelpforum