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Substitute p=x^2

  1. Apr 16, 2009 #1

    nameVoid

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    is there a way to solve this by hand
    (1/2)x^4-x^2-1=0
     
    nameVoid, Apr 16, 2009
  2. jcsd
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  3. Apr 16, 2009 #2

    Cyosis

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    Re: solve

    Yes substitute p=x^2.
     
    Cyosis, Apr 16, 2009
  4. Apr 16, 2009 #3

    nameVoid

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    Re: solve

    (1/2)x^4-x^2-1=(1/2)p^2-p-1=0

    quadratic in p

    [1+||- (1+2)^(1/2) ] = 1+||-3^(1/2) = p = x^2

    x=+||-[1+||-3^(1/2) ]^(1/2) =+||-[1+3^(1/2) ]^(1/2)
     
    nameVoid, Apr 16, 2009
  5. Apr 16, 2009 #4

    Cyosis

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    Re: solve

    That's correct.
     
    Cyosis, Apr 16, 2009
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