MathDB
Another very common inequality

Source: Bosnia and Herzegovina Team Selection Test 2005 problem 2 day 1

October 6, 2017
algebraInequalitythree variable inequality

Problem Statement

If a1a_1, a2a_2 and a3a_3 are nonnegative real numbers for which a1+a2+a3=1a_1+a_2+a_3=1, then prove the inequality a1a2+a2a3+a3a1≤13a_1\sqrt{a_2}+a_2\sqrt{a_3}+a_3\sqrt{a_1}\leq \frac{1}{\sqrt{3}}
Back to ProblemsView on AoPS