Problem 15

$\large \dfrac{a^3+2}{b^2+1}+\dfrac{b^3+2}{c^2+1}+\dfrac{c^3+2}{a^2+1}$

Given that $\large 0\leq a,b,c\leq 1$ . Let the maximum value of the expression above is $A$ . The sum of $a,b$ and $c$ when the equality holds is $B$ . Compute $\large AB(A+B)$ .

Note : You don't need to try $a=b=c$ . Because it isn't the answer.

This problem is in this Set .