# Problem 15

Algebra Level 5

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

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.

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