Inspired by Harsh Shrivastava

Algebra Level 2

{x+y+z=4x2+y2+z2=6\large{\begin{cases} x + y + z &= 4 \\ x^2 + y^2 + z^2 &= 6 \end{cases} }

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

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