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Math Help - algebra problem

  1. #1
    Junior Member
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    algebra problem

    Let a and b be positive real numbers. Prove that

    (a+2)(b+2)(a+b) > 16ab
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    By AM–GM,

    a+2\ \ge\ 2\sqrt{2a}

    b+2\ \ge\ 2\sqrt{2b}

    a+b\ \ge\ 2\sqrt{ab}

    The result follows.
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