MathDB
Problems
Contests
International Contests
Tuymaada Olympiad
2022 Tuymaada Olympiad
4
6 variable inequality on 4th roots
6 variable inequality on 4th roots
Source: Tuymaada Olympiad 2022 Senior Category Problem 4
July 7, 2022
Inequality
inequalities
Problem Statement
For every positive
a
1
,
a
2
,
…
,
a
6
a_1, a_2, \dots, a_6
a
1
,
a
2
,
…
,
a
6
, prove the inequality
a
1
a
2
+
a
3
+
a
4
4
+
a
2
a
3
+
a
4
+
a
5
4
+
⋯
+
a
6
a
1
+
a
2
+
a
3
4
≥
2
\sqrt[4]{\frac{a_1}{a_2 + a_3 + a_4}} + \sqrt[4]{\frac{a_2}{a_3 + a_4 + a_5}} + \dots + \sqrt[4]{\frac{a_6}{a_1 + a_2 + a_3}} \ge 2
4
a
2
+
a
3
+
a
4
a
1
+
4
a
3
+
a
4
+
a
5
a
2
+
⋯
+
4
a
1
+
a
2
+
a
3
a
6
≥
2
Back to Problems
View on AoPS