KöMaL 2006 A414

Prove $(xy+yz+zx) \left(\frac 1{{(x+y)}^2}+\frac1{{(y+z)}^2}+\frac1{{(z+x)}^2}\right) \ge\frac94$ for all positive reals $x$ , $y$ , $z$ .

Official text KöMaL. Quoted with source.

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