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Kazakhstan Contests
Kazakhstan National Olympiad
2005 Kazakhstan National Olympiad
2
a+b+c+2=abc
a+b+c+2=abc
Source: Kazakhstan NMO 2005 (Final round) P2
December 16, 2014
inequalities
inequalities proposed
Kazakhstan
Problem Statement
Prove that
a
b
+
b
c
+
c
a
≥
2
(
a
+
b
+
c
)
ab+bc+ca\ge 2(a+b+c)
ab
+
b
c
+
c
a
≥
2
(
a
+
b
+
c
)
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive reals such that
a
+
b
+
c
+
2
=
a
b
c
a+b+c+2=abc
a
+
b
+
c
+
2
=
ab
c
.
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