A diagram for inequalities of symmetric functions. Issue 558 (November 2019)

• Record Type: Journal Article
• Authors: Dolan, Stan
• Is Part Of: Mathematical gazette. Volume 103:Issue 558(2019)
• Page Start: 461
• Page End: 470
• Publication Date: 2019-11
• Subjects: Mathematics -- Periodicals; Mathématique; Mathematik; Mathematics; Periodicals; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); Zeitschrift; Online-Publikation; 510
• DOI: 10.1017/mag.2019.105
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : Consider the problem of proving that, for any positive numbers x, y and z, $${\rm{9 (}}{{\rm{x}}^{\rm{3}}}{\rm{ + }}{{\rm{y}}^{\rm{3}}}{\rm{ + }}{{\rm{z}}^{\rm{3}}}{\rm{) }} \ge {\rm{ (x + y + z}}{{\rm{)}}^{\rm{3}}}{\rm{ }}{\rm{.}}$$ This is an example of a type of inequality that frequently occurs in Olympiad-style problems, [1]. These problems may involve symmetric functions of more or fewer variables than the three used here. However, three variables are commonly used and appear to give appropriately difficult problems without making excessive computational demands.