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Moldova Contests
JBMO TST - Moldova
2012 Junior Balkan Team Selection Tests - Moldova
2
Does there exist
Does there exist
Source:
August 9, 2012
floor function
inequalities proposed
inequalities
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be positive real numbers and
c
d
=
1
cd=1
c
d
=
1
. Prove that there exists a positive integer
n
n
n
such that
a
b
≤
n
2
≤
(
a
+
c
)
(
b
+
d
)
ab\leq n^2\leq (a+c)(b+d)
ab
≤
n
2
≤
(
a
+
c
)
(
b
+
d
)
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