Cool Inequality 10 Trouble some

Algebra Level 4

(xy+yz+zx)(1(x+y)2+1(y+z)2+1(z+x)2){\sqrt { \left( xy+yz+zx \right) \left( \frac { 1 }{ \left( x+y \right) ^{ 2 } } +\frac { 1 }{ \left( y+z \right) ^{ 2 } } +\frac { 1 }{ { \left( z+x \right) }^{ 2 } } \right) } }

If x,yx,y and zz are positive reals, find the minimum value of the expression above.

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