Problem 6

Algebra Level 5

\[\large \frac{abc(a+b+c)}{(a^2+b^2+c^2)^2}\]

Given that \(a,b,c\) are reals and are non-zero number at the same time and \(a^3b+b^3c+c^3a=0\). Let the maximum value of the expression above be \( A\). Compute \(\left \lfloor 60000A \right \rfloor\).


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