# Inspired by Harsh Shrivastava

Algebra Level 2

$\large{\begin{cases} x + y + z &= 4 \\ x^2 + y^2 + z^2 &= 6 \end{cases} }$

If $$x, y, z$$ are three real numbers satisfying the above system of equations, then find the maximum value of $$xyz$$.

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