MathDB
Not homogenous, messy inequality

Source: Latvian TST for Baltic Way 2019 Problem 1

May 29, 2020
inequalities

Problem Statement

Prove that for all positive real numbers a,b,ca, b, c with 1a+1b+1c=1\frac{1}{a}+\frac{1}{b}+\frac{1}{c} =1 the following inequality holds: 3(ab+bc+ca)+9a+b+c≤9abca+b+c+2(a2+b2+c2)+13(ab+bc+ca)+\frac{9}{a+b+c} \le \frac{9abc}{a+b+c} + 2(a^2+b^2+c^2)+1
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