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Math Help - Find x(u,v) and y(u,v) .

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    Question Find x(u,v) and y(u,v) .

    given
    u=y-x
    v=xy

    Find x(u,v) and y(u,v) .

    Thank you.
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  2. #2
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    Quote Originally Posted by kittycat View Post
    given
    u=y-x
    v=xy

    Find x(u,v) and y(u,v) .

    Thank you.
    Use substitution:
    y = u + x

    Thus
    v = x(u + x)

    x^2 + ux - v = 0

    So
    x = \frac{-u \pm \sqrt{u^2 + 4v}}{2}

    Thus
    y = u + \frac{-u \pm \sqrt{u^2 + 4v}}{2} = \frac{u \pm \sqrt{u^2 + 4v}}{2}

    Which of the "+" or "-" signs to use is going to depend on the specific nature of the problem where the u and v come from. At this stage all we can say is that there are two acceptable solutions.

    -Dan
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