An algebra problem by Dev Sharma

Algebra Level 5

{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}}

If x,yx,y and zz are complex numbers that satisfy the system of equations above and x2+y2+z2>0x^2 + y^2 + z^2 > 0 , find the value of x10+y10+z10x^{10} + y^{10} + z^{10} .

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