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Contests
National and Regional Contests
India Contests
India National Olympiad
2001 India National Olympiad
3
One on reals
One on reals
Source: INMO 2001 Problem 3
October 10, 2005
inequalities
logarithms
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers such that
a
b
c
=
1
abc= 1
ab
c
=
1
, Prove that
a
b
+
c
b
c
+
a
c
a
+
b
≤
1.
a^{b+c} b^{c+a} c^{a+b} \leq 1 .
a
b
+
c
b
c
+
a
c
a
+
b
≤
1.
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