MathDB
Problems
Contests
National and Regional Contests
Kazakhstan Contests
Kazakhstan National Olympiad
2018 Kazakhstan National Olympiad
4
4
Part of
2018 Kazakhstan National Olympiad
Problems
(1)
Kazakhstan MO 2018 inequality
Source: Kazakhstan MO 2018 final round.Grade 11;Problem 4
5/4/2018
Prove that for all reas
a
,
b
,
c
,
d
∈
(
0
,
1
)
a,b,c,d\in(0,1)
a
,
b
,
c
,
d
∈
(
0
,
1
)
we have
(
a
b
−
c
d
)
(
a
c
+
b
d
)
(
a
d
−
b
c
)
+
min
(
a
,
b
,
c
,
d
)
<
1.
\left(ab-cd\right)\left(ac+bd\right)\left(ad-bc\right)+\min{\left(a,b,c,d\right)} < 1.
(
ab
−
c
d
)
(
a
c
+
b
d
)
(
a
d
−
b
c
)
+
min
(
a
,
b
,
c
,
d
)
<
1.
inequalities
algebra
analysis
Kazakhstan