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- Feb 14, 2012

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Let $a$, $b$, $c$, $d$ and $e$ be strictly positive real numbers such that:

\(\displaystyle a^2+b^2+c^2=d^2+e^2\)

\(\displaystyle a^4+b^4+c^4=d^4+e^4\)

Compare \(\displaystyle a^3+b^3+c^3\) with \(\displaystyle d^3+e^3\).

I have been exhausting all kinds of algebraic tricks, but I still don't get anywhere near to cracking it, and it is so frustrating not knowing how to solve it...

Any help and/or suggestions toward how to solve this problem is much appreciated.