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 \( \left( x+y+z \right) ^{12}? \)

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