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2010 JBMO Shortlist
4
Inequality
Inequality
Source:
June 28, 2016
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be real positive numbers such that
a
b
c
(
a
+
b
+
c
)
=
3
abc(a+b+c)=3
ab
c
(
a
+
b
+
c
)
=
3
Prove that
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
8
(a+b)(b+c)(c+a) \geq 8
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
≥
8
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