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Turkey MO (2nd round)
1998 Turkey MO (2nd round)
2
An Easy Inequality on three variables
An Easy Inequality on three variables
Source: Turkish NMO 1998, 2. Problem
July 31, 2011
inequalities
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inequalities proposed
Problem Statement
If
0
≤
a
≤
b
≤
c
0\le a\le b\le c
0
≤
a
≤
b
≤
c
real numbers, 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
.
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