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Math Help - Equations Reducible To Quadratics

  1. #1
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    Equations Reducible To Quadratics

    For x^4 - 8x^2-4= 0 ,

    Does x work out to be = +/-√(4+/-2√5)

    N.B. +/- means + or -

    I've subbed in my answer but it doesnt seem to work. I've tried finding x using quadratic formula and completing the square.

    Can anyone please help?
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  2. #2
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    Hello,

    I think you are doing the right thing. Just one word: since 4-2\sqrt{5}<0, \pm\sqrt{4-2\sqrt{5}} are imaginary numbers.

    Bye.
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  3. #3
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    Quote Originally Posted by xwrathbringerx View Post
    For x^4 - 8x^2-4= 0 ,

    Does x work out to be = +/-√(4+/-2√5)

    N.B. +/- means + or -

    I've subbed in my answer but it doesnt seem to work. I've tried finding x using quadratic formula and completing the square.

    Can anyone please help?
    Here's how it's solved...

    x^4 - 8x^2 - 4 = 0.

    Let X = x^2.

    So we have X^2 - 8X - 4 = 0.

    Using the Quadratic formula x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} we find

    X = \frac{8 \pm \sqrt{64 + 16}}{2} = \frac{8 \pm \sqrt{80}}{2}

     = \frac{8 \pm 4\sqrt{5}}{2} = 4 + 2\sqrt{5} or 4 - 2\sqrt{5}.


    Since x^2 = X we have

    x^2 = 4 + 2\sqrt{5} or x^2 = 4 - 2\sqrt{5}.


    So x = \pm \sqrt{4 \pm 2\sqrt{5}}.

    So yes, you're right.
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