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India Contests
Regional Mathematical Olympiad
1993 India Regional Mathematical Olympiad
6
A veeeery simple inequality
A veeeery simple inequality
Source:
October 23, 2005
inequalities
algebra
Problem Statement
If
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are four positive reals such that
a
b
c
d
=
1
abcd= 1
ab
c
d
=
1
, prove that
(
1
+
a
)
(
1
+
b
)
(
1
+
c
)
(
1
+
d
)
≥
16.
(1+a) (1+b) (1 +c ) (1 +d ) \geq 16.
(
1
+
a
)
(
1
+
b
)
(
1
+
c
)
(
1
+
d
)
≥
16.
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