MathDB
\sqrt{a^2+bc} + \sqrt{b^2+ac} + \sqrt{c^2+ab} <= 3 if a + b + c <= 2.

Source: 2013 Brazil Team Selection Test 4.4

July 23, 2021
inequalities

Problem Statement

Let a,b,ca, b, c be non-negative reals with a+b+c≤2a + b + c \le 2. prove that b2+ac+a2+bc+c2+ab≤3\sqrt{b^2+ac} + \sqrt{a^2+bc} + \sqrt{c^2+ab} \le 3
Back to ProblemsView on AoPS