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Math Help - solving equation

  1. #1
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    solving equation

    Hello.. I'm not sure whether this should be posted under here:

    What is the standard method to solve for the following equation:
    4x^4-x-9=0
    without using software.

    Thanks!
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Last edited by ADARSH; April 16th 2009 at 01:22 AM.
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  3. #3
    Senior Member Twig's Avatar
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    Are you sure itīs not supposed to be  4x^{4} -x^{2} -9 = 0
    That would simplify things..
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  4. #4
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    That's the equation.. Thanks for the link too.. but it's so difficult.. wondering anyone with the software can help me with the 4 roots?
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  5. #5
    Senior Member Twig's Avatar
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    hi

    Did u mean its supposed to be an  x^2 term?

    In this case:

    let x^2 = t

    Giving us:  4t^2 -t -9 = 0

    Which can be written:  (t-\frac{1}{8})^{2} = \frac{145}{8}

    Solving gives:  t_{1} = \frac{1+\sqrt{145}}{8}
     t_{2} = \frac{1-\sqrt{145}}{8}

    But we have  x^2 = t , so two solutions are:
     \sqrt{\frac{1+\sqrt{145}}{8}} \mbox{ and } -\sqrt{\frac{1+\sqrt{145}}{8}}

    You will also get two imaginary roots, but I donīt write them out here...

    Btw: If you DID mean 4x^4-x-9 = 0, Mathematica gives me a HORRIBLE answer...
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