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min of \sqrt{2+x}+\sqrt{2+y}+\sqrt{2+z}+\sqrt{x+y}+\sqrt{y+z}+\sqrt{z+x}

Source: 2022 Greece JBMO TST p3

November 3, 2022

algebrainequalities

Problem Statement

The real numbers

x,y,z

are such that

x+y+z=4

and

0 \le x,y,z \le 2

. Find the minimun value of the expression

A=\sqrt{2+x}+\sqrt{2+y}+\sqrt{2+z}+\sqrt{x+y}+\sqrt{y+z}+\sqrt{z+x}