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North Macedonia Contests
JBMO TST - Macedonia
2012 JBMO TST - Macedonia
3
Macedonian JBMO TST 2012 - Problem 3
Macedonian JBMO TST 2012 - Problem 3
Source: Macedonian JBMO TST 2012
August 27, 2012
inequalities
inequalities proposed
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
be positive real numbers and
a
+
b
+
c
+
2
=
a
b
c
a+b+c+2=abc
a
+
b
+
c
+
2
=
ab
c
. Prove that
a
b
+
1
+
b
c
+
1
+
c
a
+
1
≥
2.
\frac{a}{b+1}+\frac{b}{c+1}+\frac{c}{a+1}\geq{2}.
b
+
1
a
+
c
+
1
b
+
a
+
1
c
≥
2
.
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