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2017 Silk Road
3
3
Part of
2017 Silk Road
Problems
(1)
Inequality
Source: Silk Road Mathematival Competition , P3
5/25/2017
Prove that among any
42
42
42
numbers from the interval
[
1
,
1
0
6
]
[1,10^6]
[
1
,
1
0
6
]
, you can choose four numbers so that for any permutation
(
a
,
b
,
c
,
d
)
(a, b, c, d)
(
a
,
b
,
c
,
d
)
of these numbers, the inequality
25
(
a
b
+
c
d
)
(
a
d
+
b
c
)
≥
16
(
a
c
+
b
d
)
2
25 (ab + cd) (ad + bc) \ge 16 (ac + bd)^ 2
25
(
ab
+
c
d
)
(
a
d
+
b
c
)
≥
16
(
a
c
+
b
d
)
2
holds.
inequalities proposed
inequalities
srmc