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Math Help - Substition transformation to quadratic form

  1. #1
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    Substition transformation to quadratic form

     <br />
\frac{\1}{2x-1}^2 + \frac{\1}{2x-1}^2 -12=0<br />

    Apologies for the sloppy LaTex formatting. There should be parentheses around the fractions indicating that both need to be squared.

    I think my first issue lies with squaring the fraction. If I could do that I'd be on the way. I don't normally ask to be spoon fed an answer but in this case... Thanks in advance for any all help.
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  2. #2
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    Re: Substition transformation to quadratic form

    \displaystyle \left(\frac{1}{2x-1}\right)^2+\left(\frac{1}{2x-1}\right)^2-12=0

    \displaystyle 2\left(\frac{1}{2x-1}\right)^2-12=0

    \displaystyle 2\left(\frac{1}{2x-1}\right)^2=12

    Now divide both sides by 2 and take the square root, that should get you pretty close to the end.

    What do you get?
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  3. #3
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    Re: Substition transformation to quadratic form

    Since you titled this "Substitution transformation to quadratic form", use the substitution u= \frac{1}{2x- 1} so your equation becomes u^2+ u^2- 12= 2u^2- 12= 0
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