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MathLinks Contest 4th
7.1
0471 inequalites 4th edition Round 7 p1
0471 inequalites 4th edition Round 7 p1
Source:
May 7, 2021
inequalities
algebra
4th edition
Problem Statement
Let
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
be positive reals such that
a
b
c
d
=
1
abcd = 1
ab
c
d
=
1
. Prove that
1
a
(
b
+
1
)
+
1
b
(
c
+
1
)
+
1
c
(
d
+
1
)
+
1
d
(
a
+
1
)
≥
2.
\frac{1}{a(b + 1)} +\frac{1}{b(c + 1)} +\frac{1}{c(d + 1)} +\frac{1}{d(a + 1)} \ge 2.
a
(
b
+
1
)
1
+
b
(
c
+
1
)
1
+
c
(
d
+
1
)
1
+
d
(
a
+
1
)
1
≥
2.
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