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Math Help - x^4-x^2+2=0 Solve. Need help :(

  1. #1
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    x^4-4x^2+2=0

    Hey all, the problem in the title is what has me confused. i know there are solutions, but I do not know how to arrive at the solution. Maybe a step by step, or even a website explaining how to solve this type of problem would be very helpful. Thanks : )

    Thanks for helping me icemanfan, I really appreciate the time you took to help me. I made a mistake in my original equation, and for that I am truly sorry. The correct equation is x^4-4x^2+2=0. Again, I'm sorry
    Last edited by mochabla; October 6th 2008 at 05:27 PM.
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  2. #2
    MHF Contributor
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    x^4 - x^2 + 2 = 0

    Substitute u = x^2. Then the equation becomes:

    u^2 - u + 2 = 0

    By the quadratic equation:

    u = \frac{1 \pm \sqrt{(-1)^2 - 4(1)(2)}}{2}

    u = \frac{1 \pm \sqrt{-7}}{2}

    So u is a complex number.

    Since u = x^2 has no real solutions in x, the original equation has no real solutions in x.
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  3. #3
    Super Member 11rdc11's Avatar
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    Still follow icemanfan suggestion but just change it too

    u^2 - 4u + 2~=~0

    u = \frac{4 \pm \sqrt{(-4)^2 - 4(1)(2)}}{2}
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