# Thread: Prove positive real numbers a,b,c.

1. ## Re: Prove positive real numbers a,b,c.

Originally Posted by pikachu26134
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??

2. ## 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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