MathDB
(a-b) (b-c) (c-d) (d-a) + (a-c)^2 (b-d)^2 >= 0

Source: problem 6 (U1) of QEDMO 1; originally created by Vlad Bazon

November 7, 2005
inequalitiesinequalities proposed

Problem Statement

Prove that for any four real numbers aa, bb, cc, dd, the inequality (a−b)(b−c)(c−d)(d−a)+(a−c)2(b−d)2≥0 \left(a-b\right)\left(b-c\right)\left(c-d\right)\left(d-a\right)+\left(a-c\right)^2\left(b-d\right)^2\geq 0 holds. [hide="comment"]This is inequality (350) in: Mihai Onucu Drimbe, Inegalitati, idei si metode, Zalau: Gil, 2003.
Posted here only for the sake of completeness; in fact, it is more or less the same as http://www.mathlinks.ro/Forum/viewtopic.php?t=3152 . Darij
Back to ProblemsView on AoPS