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Problems
Contests
National and Regional Contests
Greece Contests
Greece JBMO TST
2022 Greece JBMO TST
3
3
Part of
2022 Greece JBMO TST
Problems
(1)
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
11/3/2022
The real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
are such that
x
+
y
+
z
=
4
x+y+z=4
x
+
y
+
z
=
4
and
0
≤
x
,
y
,
z
≤
2
0 \le x,y,z \le 2
0
≤
x
,
y
,
z
≤
2
. Find the minimun value of the expression
A
=
2
+
x
+
2
+
y
+
2
+
z
+
x
+
y
+
y
+
z
+
z
+
x
A=\sqrt{2+x}+\sqrt{2+y}+\sqrt{2+z}+\sqrt{x+y}+\sqrt{y+z}+\sqrt{z+x}
A
=
2
+
x
+
2
+
y
+
2
+
z
+
x
+
y
+
y
+
z
+
z
+
x
.
algebra
inequalities