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    solve eq

    solve the equations simuntaneousely [1] X +square root of y=11 [2] square root of x+y=7
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    Quote Originally Posted by zaki View Post
    solve the equations simuntaneousely [1] X +square root of y=11 [2] square root of x+y=7
    Just for completeness here:
    $\displaystyle x + \sqrt{y} = 11$
    and
    $\displaystyle \sqrt{x} + y = 7$

    From the bottom equation:
    $\displaystyle y = 7 - \sqrt{x}$

    Inserting this into the top equation:
    $\displaystyle x + \sqrt{7 - \sqrt{x}} = 11$

    $\displaystyle \sqrt{7 - \sqrt{x}} = 11 - x$<-- Square both sides

    Since the solution is going to turn out to be ugly anyway, I'm going to use a trick. (They use it in the referred thread as well.)
    $\displaystyle 7 - \sqrt{x} = (11 - x)^2$

    $\displaystyle \sqrt{x} = x^2 - 22x + 114$

    $\displaystyle x = (x^2 - 22x + 114)^2$

    $\displaystyle x = x^4 - 44x^3 + 712x^2 - 5016x + 12996$

    $\displaystyle x^4 - 44x^3 + 712x^2 - 5017x + 12996 = 0$

    Using the rational root theorem, you can find one nice solution: x = 9. You can get the rest numerically: x = 7.86869, 12.8481, 14.2832.

    Thus
    $\displaystyle y = 7 - \sqrt{x}$

    So
    $\displaystyle (x, y) = (7.86869, 4.19488), (9, 4), (12.8481, 3.41557), \text{ and } (14.2832, 3.22069)$

    -Dan
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