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Math Help - need help

  1. #1
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    Question need help

    need your help!

    we have u=y/x and v=xy

    how to solve x and y in terms of u and v ?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kittycat View Post
    need your help!

    we have u=y/x and v=xy

    how to solve x and y in terms of u and v ?
    u = \frac yx ......................(1)
    v = xy .....................(2)

    \Rightarrow y = xu ................from equation (1)

    \Rightarrow y = \frac vy \cdot u .............solved for x in equation (2) and plugged it in.

    \Rightarrow y^2 = uv

    \Rightarrow y = \sqrt {uv}

    now solve for x in a similar manner
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  3. #3
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    Hello, kittycat!

    Another approach . . .


    Given: . u \:=\:\frac{y}{x},\;\;\;v\:=\:xy

    Solve for x and y in terms of u and v.

    We have: . \begin{array}{cccc}\frac{y}{x} & = & u & {\color{blue}[1]} \\ xy & = & v & {\color{blue}[2]} \end{array}

    Divide [1] by [2]: . \frac{\frac{y}{x}}{xy} \:=\:\frac{u}{v}\quad\Rightarrow\quad\frac{1}{x^2}  \:=\:\frac{u}{v}\quad\Rightarrow\quad x^2\:=\:\frac{v}{u}\quad\Rightarrow\quad\boxed{ x \:=\:\sqrt{\frac{v}{u}}}

    Multiply [1] and [2]: . \frac{y}{x}\cdot xy \:=\:uv\quad\Rightarrow\quad y^2\:=\:uv\quad\Rightarrow\quad\boxed{ y \:=\:\sqrt{uv}}

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