# Problem 5

Algebra Level 5

$\frac{8a+3b+4(\sqrt{ab}+\sqrt{bc}+\sqrt[3]{abc})}{1+(a+b+c)^2}$

Given that $$a,b,c$$ are positive reals. If the maximum value of the expression above can be expressed as $$\large \frac{m}{n}$$ where $$m,n$$ are coprime integers.Find $$m+n$$.

This problem is in this Set.

×