MathDB
Prove this cyclic inequality

Source: 2019 Jozsef Wildt International Math Competition

May 19, 2020
inequalitiescyclic inequality

Problem Statement

Let aa, bb, c∈(0,+∞)c \in (0,+\infty) . Then the following inequality is true:(a+b)(b+c)+(b+c)(c+a)+(c+a)(a+b)+a+b+c≤(ab+bc+ca)(1ab+1bc+1ca)\sqrt{(a+b)(b+c)}+\sqrt{(b+c)(c+a)}+\sqrt{(c+a)(a+b)}+a+b+c\leq \left(ab+bc+ca\right)\left(\frac{1}{\sqrt{ab}}+\frac{1}{\sqrt{bc}}+\frac{1}{\sqrt{ca}}\right)
Back to ProblemsView on AoPS