Apply Vieta's?

Algebra Level 5

{a+b+c=0a2+b2+c2=1\large{\begin{cases} a+b+c = 0 \\ a^{2}+b^{2}+c^{2} = 1 \end{cases} }

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

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