MathDB

(a^2b^2)/(a+b)+(b^2c^2)/(b+c)+(c^2a^2)/(c+a) <=(a^3+b^3+c^3)/2

Source: Greece JBMO TST 2008 p2

April 29, 2019

algebrainequalitiesthree variable inequality

Problem Statement

a,b,c

are positive real numbers, prove that

\frac{a^2b^2}{a+b}+\frac{b^2c^2}{b+c}+\frac{c^2a^2}{c+a}\le \frac{a^3+b^3+c^3}{2}