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Math Help - Solving a simple equation

  1. #1
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    Solving a simple equation

    My friend asked me for math help for her pre-calc class and I can't for the life of me do the problem--- I'm out of practice.

    Solve for x:

    x^4-3x^2+2=0.
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  2. #2
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    Quote Originally Posted by jelloish View Post
    Solve for x:
    x^4-3x^2+2=0.
    Let k = x^2
    k^2 - 3k + 2 = 0
    Solve that for k, then for x
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  3. #3
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    Hi

    What is needed here is some simple substitution

    you have

     x^4-3x^2+2 = 0

    Replace x^2 with a dummy variable, lets call it a

    Now  x^4-3x^2+2 = 0 becomes  a^2-3a+2 = 0

    This is a simple quadratic

     a^2-3a+2 = 0

     (a-2)(a-1)= 0

    By the null factor law

     a = 1,2

    but we are after x so

     x^2 = 1,2 \Rightarrow x = \pm 1,\pm \sqrt{2}
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  4. #4
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    Okay so when solving it that way I got K being -2 and -1, which then makes x= 2 and 1. However when put back into the equation it doesn't solve it correctly.

    Then again I'm doing this all in my head and without pen+paper.
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  5. #5
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    It shouldn't, that is the solution for k.

    My post gives a detailed answer, try the solutions x = \pm 1,\pm \sqrt{2}

    these will work.
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  6. #6
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    I still tried those and they aren't working.

    When substituting 2 (for all intents and purposes it works for the -2 too because of the squaring...) the equation ends up being

    2^4 - 3(2^2) +2 which is..

    16-12+2

    which is 6.

    The 1, -1 do work, though. My brains are frieeeeed.
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  7. #7
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    Oh boy... I forgot that it was a root two.

    Thanks. hahaha
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