This is the last problem of Newton's Sums I'll post

Algebra Level 4

Given that xx, yy and zz are complex numbers such that:

x+y+z=3x+y+z=3

x3+y3+z3=15x^3+y^3+z^3=15

x4+y4+z4=35x^4+y^4+z^4=35

Find the sum of all the possible values of x2(x3+1)+y2(y3+1)+z2(z3+1)x^2(x^3+1)+y^2(y^3+1)+z^2(z^3+1).

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