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Math Help - inequality proof

  1. #1
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    inequality proof

    Q. For real numbers a,b,c if a+b+c=1 then prove that ab + bc + ca < or = 1/3.
    Last edited by CaptainBlack; November 10th 2010 at 09:59 PM.
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  2. #2
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    Quote Originally Posted by akshay1995 View Post
    Q. For real numbers a,b,c if a+b+c=1 then prove that ab + bc + ca < or = 1/3.
    Square both sides of a+b+c=1 and derive an expression for a^{2}+b^{2}+c^{2}.

    Next, expand (a-b)^{2}+(b-c)^{2}+(c-a)^{2}\geq 0, and derive an inequality for a^{2}+b^{2}+c^{2}.

    Combine the two, and the required result follows.
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