MathDB
Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine National Mathematical Olympiad
1999 Ukraine National Mathematical Olympiad
Problem 7
Ukraine 1999
Ukraine 1999
Source:
December 25, 2014
inequalities unsolved
inequalities
Problem Statement
If
x
1
x_1
x
1
,
x
2
x_2
x
2
, ...,
x
6
x_6
x
6
∈
\in
∈
[
0
,
1
]
[0,1]
[
0
,
1
]
, prove that the cyclic sum of
x
1
3
x
2
5
+
x
3
5
+
x
4
5
+
x
5
5
+
x
6
5
+
5
\frac{x_1^3}{x_2^5+x_3^5+x_4^5+x_5^5+x_6^5+5}
x
2
5
+
x
3
5
+
x
4
5
+
x
5
5
+
x
6
5
+
5
x
1
3
is less than
3
5
\frac{3}{5}
5
3
.
Back to Problems
View on AoPS