MathDB
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National and Regional Contests
India Contests
Postal Coaching
2011 Postal Coaching
4
Inequality with three positive reals of product 1
Inequality with three positive reals of product 1
Source:
December 31, 2011
inequalities
inequalities unsolved
Problem Statement
For all
a
,
b
,
c
>
0
a, b, c > 0
a
,
b
,
c
>
0
and
a
b
c
=
1
abc = 1
ab
c
=
1
, prove that
1
a
(
a
+
1
)
+
a
b
(
a
b
+
1
)
+
1
b
(
b
+
1
)
+
b
c
(
b
c
+
1
)
+
1
c
(
c
+
1
)
+
c
a
(
c
a
+
1
)
≥
3
4
\frac{1}{a(a+1)+ab(ab+1)}+\frac{1}{b(b+1)+bc(bc+1)}+\frac{1}{c(c+1)+ca(ca+1)}\ge\frac{3}{4}
a
(
a
+
1
)
+
ab
(
ab
+
1
)
1
+
b
(
b
+
1
)
+
b
c
(
b
c
+
1
)
1
+
c
(
c
+
1
)
+
c
a
(
c
a
+
1
)
1
≥
4
3
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