MathDB
Problems
Contests
International Contests
Rioplatense Mathematical Olympiad, Level 3
2013 Rioplatense Mathematical Olympiad, Level 3
1
Rioplatense Olympiad 2013, Level 3, Problem 1
Rioplatense Olympiad 2013, Level 3, Problem 1
Source:
August 23, 2014
inequalities proposed
inequalities
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be real positive numbers such that
a
2
+
b
2
+
c
2
+
d
2
=
1
a^2+b^2+c^2+d^2 = 1
a
2
+
b
2
+
c
2
+
d
2
=
1
. Prove that
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
(
1
−
d
)
≥
a
b
c
d
(1-a)(1-b)(1-c)(1-d) \geq abcd
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
(
1
−
d
)
≥
ab
c
d
.
Back to Problems
View on AoPS