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1997 Tournament Of Towns
(544) 5
TOT 544 1997 Spring S A5 sum 1/(1+a+b) <1
TOT 544 1997 Spring S A5 sum 1/(1+a+b) <1
Source:
September 11, 2024
algebra
number theory
inequalities
Problem Statement
Prove that
1
1
+
a
+
b
+
1
1
+
b
+
c
+
1
1
+
c
+
a
<
1
\frac{1}{1+a+b}+\frac{1}{1+b+c}+\frac{1}{1+c+a} <1
1
+
a
+
b
1
+
1
+
b
+
c
1
+
1
+
c
+
a
1
<
1
where
a
,
b
a, b
a
,
b
and
c
c
c
are positive numbers such that
a
b
c
=
1
abc = 1
ab
c
=
1
.(G Galperin)
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