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Math Help - Qudratic equations???

  1. #1
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    Qudratic equations???

    √x/(x – 1) + √(x – 1)/x = 2(1/6)

    Please find solution for x(with steps), I find it very difficult especially with the unnecessary roots I find even after squaring!!!!

    the answer is : x = - 4/5, 9/5
    Last edited by ice_syncer; July 2nd 2008 at 01:38 AM.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by ice_syncer View Post
    √x/(x – 1) + √(x – 1)/x = 2(1/6)

    Please find solution for x, I find it very difficult especially with the unnecessary roots I find even after squaring!!!!
    Is it \frac{\sqrt{x}}{x-1}+\frac{\sqrt{x-1}}{x}=\frac{2}{6} (that's what you wrote) or \sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{2}{6} ?
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    Quote Originally Posted by flyingsquirrel View Post
    Hi


    Is it \frac{\sqrt{x}}{x-1}+\frac{\sqrt{x-1}}{x}=\frac{2}{6} (that's what you wrote) or \sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{2}{6} ?

    well, actually that's exactly what the assignment says

    √x/(x 1) + √(x 1)/x = 2(1/6)

    I'm guessing it's your first option...but the answer key says the answer for this is
    :
    x = - 4/5, 9/5
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  4. #4
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    Quote Originally Posted by ice_syncer View Post
    √x/(x – 1) + √(x – 1)/x = 2(1/6)

    Please find solution for x(with steps), I find it very difficult especially with the unnecessary roots I find even after squaring!!!!

    the answer is : x = - 4/5, 9/5
    The correct equation is \sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{13}{6}.


    Square both sides:


    \frac{x}{x-1} + 2 + \frac{x-1}{x} =\frac{169}{36}.


    Multiply both sides by 36 (x - 1) x:


    36 x^2 + 72 x (x - 1) + 36 (x - 1)^2 = 169 x (x - 1)

    Expand and simplify into a routine quadratic equation. Solve the quadratic equation. Substitute the solutions into the original equation and reject the ones (if any) that fail to satisfy it.
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    Quote Originally Posted by mr fantastic View Post
    The correct equation is \sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{13}{6}.


    Square both sides:


    \frac{x}{x-1} + 2 + \frac{x-1}{x} =\frac{169}{36}.


    Multiply both sides by 36 (x - 1) x:


    36 x^2 + 72 x (x - 1) + 36 (x - 1)^2 = 169 x (x - 1)

    Expand and simplify into a routine quadratic equation. Solve the quadratic equation. Substitute the solutions into the original equation and reject the ones (if any) that fail to satisfy it.
    ok
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    The correct equation is \sqrt{\frac{x}{x-1}}+\sqrt{\frac{x-1}{x}}=\frac{13}{6}.


    Square both sides:


    \frac{x}{x-1} + 2 + \frac{x-1}{x} =\frac{169}{36}

    Subtract 2 from both sides:

    {\color{red}\Rightarrow \frac{x}{x-1} + \frac{x-1}{x} =\frac{97}{36}}


    Multiply both sides by 36 (x - 1) x:

    [snip]
    You can make life a little easier by first doing what I added (in red).
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    You can make life a little easier by first doing what I added (in red).
    yeah I did that before your requoting, thanks anyway
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