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2011 JBMO Shortlist
7
Inequality with abc=1
Inequality with abc=1
Source: JBMO 2011 Shortlist A7
May 15, 2016
inequalities
Hi
Problem Statement
A7
\boxed{\text{A7}}
A7
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive reals such that
a
b
c
=
1
abc=1
ab
c
=
1
.Prove the inequality
∑
2
a
2
+
1
a
b
+
1
a
+
1
≥
3
\sum\frac{2a^2+\frac{1}{a}}{b+\frac{1}{a}+1}\geq 3
∑
b
+
a
1
+
1
2
a
2
+
a
1
≥
3
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