Let w,x,y,z are non-negative reals such that wx \plus{} xy \plus{} yz \plus{} zw \equal{} 1.
Show that \frac {w^3}{x \plus{} y \plus{} z} \plus{} \frac {x^3}{w \plus{} y \plus{} z} \plus{} \frac {y^3}{w \plus{} x \plus{} z} \plus{} \frac {z^3}{w \plus{} x \plus{} y}\geq \frac {1}{3}. cauchy schwarzHolderInequality4-variable inequalityIMO Shortlistalgebra