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Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
1994 India Regional Mathematical Olympiad
8
An inequality
An inequality
Source: Indian RMO 1994 Problem 8
October 25, 2005
inequalities
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers such that
a
+
b
+
c
=
1
a+b+c = 1
a
+
b
+
c
=
1
, prove that
(
1
+
a
)
(
1
+
b
)
(
1
+
c
)
≥
8
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
.
(1+a)(1+b)(1+c) \geq 8 (1-a)(1-b)(1-c) .
(
1
+
a
)
(
1
+
b
)
(
1
+
c
)
≥
8
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
.
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