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.
by
Sean Ty