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Math Help - Algebra help needed on solving 2x - 3x^(-1/2) + 1 = 0

  1. #1
    s3a
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    Algebra help needed on solving 2x - 3x^(-1/2) + 1 = 0

    2x - 3x^(-1/2) + 1 = 0

    I know that when x = 1 that y or the function = 0 but I did not figure that out by myself and needed wolfram alpha to tell me. If I were to do it myself, I would have to plug in numbers which is obviously inefficient.

    My question is how do I solve it algebraically? What are the steps? I can't factor out x because there is a +1 and I can't move it to the other side because then it's no longer 0 and therefore no longer easy to figure out the values of x.

    Any help would be GREATLY appreciated!
    Thanks in advance!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    2x - 3x^{-\frac{1}{2}}+ 1 = 0

    2x-\frac{3}{\sqrt{x}}+1=0

    let \sqrt{x}=y

    x=y^2

    2y^2-\frac{3}{y}+1=0

    2y^3+y-3=0

    2y^3-2y^2+2y^2-2y+3y-3=0

    2y^2(y-1)+2y(y-1)+3(y-1)=0

    (y-1)(2y^2+2y+3)=0

    y=1

    x=1^2=1

    Thus, x=1
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