AM-GM Application

Algebra Level 3

Let x,y,zx,y,z be positive real numbers such that 1x+1y+1z=1\frac { 1 }{ x } +\frac { 1 }{ y } +\frac { 1 }{ z } =1.

Then what is the minimum value of (x1)(y1)(z1)?(x-1)(y-1)(z-1)?

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