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4
4
Part of
2021 Indonesia MO
Problems
(1)
"Can we use jensen for the test" The problem:
Source: Indonesia National Math Olympiad 2021 Problem 4 (INAMO 2021/4)
11/8/2021
Let
x
,
y
x,y
x
,
y
and
z
z
z
be positive reals such that
x
+
y
+
z
=
3
x + y + z = 3
x
+
y
+
z
=
3
. Prove that
2
x
+
y
+
2
y
+
z
+
2
z
+
x
≤
8
+
x
−
y
+
8
+
y
−
z
+
8
+
z
−
x
2 \sqrt{x + \sqrt{y}} + 2 \sqrt{y + \sqrt{z}} + 2 \sqrt{z + \sqrt{x}} \le \sqrt{8 + x - y} + \sqrt{8 + y - z} + \sqrt{8 + z - x}
2
x
+
y
+
2
y
+
z
+
2
z
+
x
≤
8
+
x
−
y
+
8
+
y
−
z
+
8
+
z
−
x
inequalities
algebra