A Basic Product

Algebra Level 4

If x,y,x, y, and zz are positive real numbers such that x+y+z=1,x + y + z = 1, find the minimum value of

(1+1x)(1+1y)(1+1z).\left( 1+\frac { 1 }{ x } \right) \left( 1+\frac { 1 }{ y } \right) \left( 1+\frac { 1 }{ z } \right) .

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