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National and Regional Contests
North Macedonia Contests
JBMO TST - Macedonia
2007 Junior Macedonian Mathematical Olympiad
3
3
Part of
2007 Junior Macedonian Mathematical Olympiad
Problems
(1)
2007 JBMO TST- Macedonia, problem 3
Source: 2007 JBMO TST- Macedonia
5/28/2019
Let
a
a
a
,
b
b
b
,
c
c
c
be real numbers such that
0
<
a
≤
b
≤
c
0 < a \le b \le c
0
<
a
≤
b
≤
c
. Prove that
(
a
+
3
b
)
(
b
+
4
c
)
(
c
+
2
a
)
≥
60
a
b
c
(a + 3b)(b + 4c)(c + 2a) \ge 60abc
(
a
+
3
b
)
(
b
+
4
c
)
(
c
+
2
a
)
≥
60
ab
c
.When does equality hold?
Junior
JMMO
2007
Macedonia
algebra
Inequality