MathDB
Problems
Contests
National and Regional Contests
Czech Republic Contests
Czech and Slovak Olympiad III A
2023 Czech and Slovak Olympiad III A.
2
SKMO 2023 P2
SKMO 2023 P2
Source: czechoslovak national mo round
April 4, 2023
combinatorics
inequalities
Problem Statement
Let
n
n
n
be a positive integer, where
n
≥
3
n \geq 3
n
≥
3
and let
a
1
,
a
2
,
.
.
.
,
a
n
a_1, a_2, ..., a_n
a
1
,
a
2
,
...
,
a
n
be the lengths of sides of some
n
n
n
-gon. Prove that
a
1
+
a
2
+
.
.
.
+
a
n
≥
2
⋅
(
a
1
2
+
a
2
2
+
.
.
.
+
a
n
2
)
a_1 + a_2 + ... + a_n \geq \sqrt{2 \cdot (a_1^2 + a_2^2 + ... + a_n^2)}
a
1
+
a
2
+
...
+
a
n
≥
2
⋅
(
a
1
2
+
a
2
2
+
...
+
a
n
2
)
Back to Problems
View on AoPS