Cool Inequality 10 Trouble some
Algebra
Level
4
\[{\sqrt { \left( xy+yz+zx \right) \left( \frac { 1 }{ \left( x+y \right) ^{ 2 } } +\frac { 1 }{ \left( y+z \right) ^{ 2 } } +\frac { 1 }{ { \left( z+x \right) }^{ 2 } } \right) } }\]
If \(x,y\) and \(z\) are positive reals, find the minimum value of the expression above.
by
Lakshya Sinha