Apply Vieta's?

Algebra Level 5

$\large{\begin{cases} a+b+c = 0 \\ a^{2}+b^{2}+c^{2} = 1 \end{cases} }$

Let $$a,b,c$$ be real numbers satisfying the above system of equations. Find the maximum possible value of $$(9abc)^2$$.

×