# Polynomial Manipulation

Algebra Level 4

If $$x, y$$ and $$z$$ satisfy $\frac { 1 }{ x } + \frac {1 }{y } + \frac {1 }{z } = 0$ $x^{2}+y^{2}+z^{2}=2,$ what is $$\left( x+y+z \right) ^{12}?$$

×