Minimize (2,1,0) with constraint (2,1,1)

Algebra Level 3

Given that xx, yy, and zz are positive real numbers satisfying xyz(x+y+z)=1xyz(x+y+z)=1, minimize (x+y)(y+z)(z+x)(x+y)(y+z)(z+x).

Enter your answer to five decimal places.

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