Inequality with wx + xy + yz + zw = 1
Source: IMO ShortList 1990, Problem 24 (THA 2)
November 2, 2005
cauchy schwarzHolderInequality4-variable inequalityIMO Shortlistalgebra
Problem Statement
Let 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}.