Make It Unequal

Algebra Level 4

\left\{ \begin{aligned} a+b+c=0\\ abc=2\\ \end{aligned} \right.

Let $$a,b$$ and $$c$$ be real numbers satisfying the system of equations above. Minimize $|a|^{3}+|b|^{3}+|c|^{3}.$

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