2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133788We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the classical entropy-power inequality (EPI). As another corollary, this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables.32 pages, 1 figureInformation Theorytext