MathDB

sum \sqrt{x+ (y-z)^2 /12 } <= \sqrt3 if x, y, z>=0, x + y + z = 1,

Source: 2004 VMEO I p1 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__vietnam_mathematical

September 26, 2021

algebrainequalities

Problem Statement

Let

x, y, z

be non-negative numbers, so that

x + y + z = 1

. Prove that

\sqrt{x+\frac{(y-z)^2}{12}}+\sqrt{y+\frac{(x-z)^2}{12}}+\sqrt{z+\frac{(x-y)^2}{12}}\le \sqrt{3}