# 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 \(xyz\).

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

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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