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Switzerland Contests
Switzerland - Final Round
2014 Switzerland - Final Round
6
An inequality
An inequality
Source: Switzerland Math Olympiad, Final round 2014, P6
June 3, 2014
inequalities
inequalities proposed
algebra
Problem Statement
Let
a
,
b
,
c
∈
R
≥
0
a,b,c\in \mathbb{R}_{\ge 0}
a
,
b
,
c
∈
R
≥
0
satisfy
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Prove the inequality :
3
−
b
a
+
1
+
a
+
1
b
+
1
+
b
+
1
c
+
1
≥
4
\frac{3-b}{a+1}+\frac{a+1}{b+1}+\frac{b+1}{c+1}\ge 4
a
+
1
3
−
b
+
b
+
1
a
+
1
+
c
+
1
b
+
1
≥
4
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