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Math Help - Solving for x

  1. #1
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    Solving for x

    Solve for x in terms of y

    y=x+\frac{1}{x}

    It was so interesting, but after 30 minutes I gave up.
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  2. #2
    Senior Member pacman's Avatar
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    y = x + 1/x



    y = x + 1/x

    xy = x^2 + 1

    x^2 - xy + 1 = 0, quadratic in x,

    x = [-(-y) +/- ((-y)^2 - 4(1)(1))^1/2]/2

    x = [y (+/-) (y^2 - 4)^(1/2)]/2

    positive root:

    x = y/2 +[sqrt (y^ - 4)]/2

    negative root;

    x = y/2 -[sqrt (y^ - 4)]/2

    plot below of y = x + 1/x
    Attached Thumbnails Attached Thumbnails Solving for x-gtr.gif  
    Last edited by pacman; September 24th 2009 at 05:27 AM.
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  3. #3
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    The above answer missed "2", it should be

    positive root:

    x = y/2 +[sqrt (y^2 - 4)]/2

    negative root;

    x = y/2 -[sqrt (y^ 2- 4)]/2
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  4. #4
    Senior Member pacman's Avatar
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    thanks woodsmith, you have an eye of the eagle
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