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Switzerland - Final Round
2023 Switzerland - Final Round
4
Inequality subject to strange conditions
Inequality subject to strange conditions
Source: Swiss MO 2023/4
March 12, 2023
inequalities
algebra
inequalities proposed
Problem Statement
Determine the smallest possible value of the expression
a
b
+
1
a
+
b
+
b
c
+
1
b
+
c
+
c
a
+
1
c
+
a
\frac{ab+1}{a+b}+\frac{bc+1}{b+c}+\frac{ca+1}{c+a}
a
+
b
ab
+
1
+
b
+
c
b
c
+
1
+
c
+
a
c
a
+
1
where
a
,
b
,
c
∈
R
a,b,c \in \mathbb{R}
a
,
b
,
c
∈
R
satisfy
a
+
b
+
c
=
−
1
a+b+c = -1
a
+
b
+
c
=
−
1
and
a
b
c
⩽
−
3
abc \leqslant -3
ab
c
⩽
−
3
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