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Math Help - Prove positive real numbers a,b,c.

  1. #31
    Senior Member abhishekkgp's Avatar
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    Re: Prove positive real numbers a,b,c.

    Quote Originally Posted by pikachu26134 View Post
    It remains to find groups abc such that that equation is true
    i didn't get that.
    i'll summarize what i want to say.
    first we showed that

    \frac{[(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3]}{[(a-b)^3+(b-c)^3+(c-a)^3]}=(a+b)(b+c)(c+a) ....(1)

    then we showed that
    (a+b)(b+c)(c+a)>8abc ......(2)

    so we have effectively shown that \frac{[(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3]}{[(a-b)^3+(b-c)^3+(c-a)^3]}>8abc
    which part, part1 or part2 as labeled above is in doubt??
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  2. #32
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    Re: Prove positive real numbers a,b,c.

    Oh cheers, you my friend are a legend. I got confused with the question. Thanks, that was really great and i now understand it!! =)
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