# Classical approach

Algebra Level 5

$\large \sum_{\text{cyc}(a,b,c)} \dfrac{a^3+b^3}{a+2b}$

Given that $$a,b$$ and $$c$$ are positive numbers satisfying $$a^2+b^2+c^2=3$$, find the minimum value of the expression above.

Submit your answer to 2 decimal places.

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