x,y,zx, y, z Polynomials

Algebra Level 3

{x+y+z=0x3+y3+z3=18x7+y7+z7=2058\large \begin{cases} x + y + z = 0 \\ x^3 + y^3 + z^3=18 \\ x^7 + y^7 + z^7=2058 \end{cases}

Given that xx, yy and zz satisfy the system of equations above, find the value of xyz.xyz.

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