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Math Help - Algebraic Errors

  1. #1
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    Algebraic Errors

    This is sample work of factorising with fractions in an inequality. I've been told that the 3rd line is incorrect, as a^2+b^2 cannot be factored over a real number. Can anyone help me determine if the factoring simply stops at the second line, or is there a correct way to continue?

    Many thanks.

    \frac{a^2+b^2}{2} \geq ab
    (a^2 + b^2/ 2) - ab >​ 0
    \frac{(a+b)(a-b)}{2}-ab\geq0
    \frac{a^2-ab+ab+b^2}{2}-ab\geq0
    \frac{a^2+b^2-2ab}{2}\geq0
    (a^2 - 2ab + b^2)/2 > 0
    \frac{(a-b)^2}{2}\geq0
    Last edited by GrigOrig99; October 24th 2012 at 07:53 AM.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Algebraic Errors

    Note that:
    (a-b)(a+b) = a^2-b^2
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  3. #3
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    Re: Algebraic Errors

    Ah, ok I see it now. Thanks.
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