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2010 JBMO Shortlist
5
xyz <= 36
xyz <= 36
Source:
October 23, 2015
inequalities
Problem Statement
Let
x
,
y
,
z
>
0
x, y, z > 0
x
,
y
,
z
>
0
with
x
≤
2
,
y
≤
3
x \leq 2, \;y \leq 3 \;
x
≤
2
,
y
≤
3
and
x
+
y
+
z
=
11
x+y+z = 11
x
+
y
+
z
=
11
Prove that
x
y
z
≤
36
xyz \leq 36
x
yz
≤
36
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