Polynomial Manipulation

Algebra Level 4

If x,y x, y and zz satisfy 1x+1y+1z=0 \frac { 1 }{ x } + \frac {1 }{y } + \frac {1 }{z } = 0 x2+y2+z2=2, x^{2}+y^{2}+z^{2}=2, what is (x+y+z)12? \left( x+y+z \right) ^{12}?

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