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Switzerland Team Selection Test
2003 Switzerland Team Selection Test
6
Simple inequality with a+b+c=2
Simple inequality with a+b+c=2
Source: Swiss IMO TST 2003
February 27, 2014
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers satisfying
a
+
b
+
c
=
2
a+b+c=2
a
+
b
+
c
=
2
. Prove the inequality
1
1
+
a
b
+
1
1
+
b
c
+
1
1
+
c
a
≥
27
13
\frac{1}{1+ab}+\frac{1}{1+bc}+\frac{1}{1+ca} \ge \frac{27}{13}
1
+
ab
1
+
1
+
b
c
1
+
1
+
c
a
1
≥
13
27
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