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

Algebra Level 4

Given that $$x$$, $$y$$ and $$z$$ are complex numbers such that:

$$x+y+z=3$$

$$x^3+y^3+z^3=15$$

$$x^4+y^4+z^4=35$$

Find the sum of all the possible values of $$x^2(x^3+1)+y^2(y^3+1)+z^2(z^3+1)$$.

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