# Yeah sure.. Newton's Sums..

Algebra Level 5

Let $$(x_1, y_1, z_1)$$, $$(x_2, y_2, z_2)$$, $$\dots$$, $$(x_n, y_n, z_n)$$ be the rational solutions to the following system of equations

$x+y+z=0 \\ x^3 + y^3 + z^3 =18 \\ x^7 + y^7 + z^7 =2058$

Evaluate:

$\sum_{i=1}^{n} x_{i}y_{i}z_{i}$

• The triple $$(a, b, c)$$ and $$(c, a, b)$$ are considered to be different.
• This problem is not entirely original.
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