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2016 JBMO Shortlist
1
Σ(ab + 4)/(a + 2) >=6 if abc = 8, a,b,c>0
Σ(ab + 4)/(a + 2) >=6 if abc = 8, a,b,c>0
Source: JBMO 2016 Shortlist A1
October 14, 2017
JBMO
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
a
b
c
=
8
abc = 8
ab
c
=
8
. Prove that
a
b
+
4
a
+
2
+
b
c
+
4
b
+
2
+
c
a
+
4
c
+
2
≥
6
\frac{ab + 4}{a + 2}+\frac{bc + 4}{b + 2}+\frac{ca + 4}{c + 2}\ge 6
a
+
2
ab
+
4
+
b
+
2
b
c
+
4
+
c
+
2
c
a
+
4
≥
6
.
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