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Contests
National and Regional Contests
Italy Contests
Italy TST
2001 Italy TST
2
0 ≤ a ≤ b ≤ c product inequality
0 ≤ a ≤ b ≤ c product inequality
Source: Italy TST 2001
November 21, 2010
inequalities
inequalities proposed
algebra
Problem Statement
Let
0
≤
a
≤
b
≤
c
0\le a\le b\le c
0
≤
a
≤
b
≤
c
be 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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