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JBMO ShortLists
2010 JBMO Shortlist
5
5
Part of
2010 JBMO Shortlist
Problems
(1)
xyz <= 36
Source:
10/23/2015
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
inequalities