MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1962 All Russian Mathematical Olympiad
019
ASU 019 All Russian MO 1962 9.2 4-variable inequality
ASU 019 All Russian MO 1962 9.2 4-variable inequality
Source:
June 17, 2019
inequalities
algebra
Problem Statement
Given a quartet of positive numbers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
, and is known, that
a
b
c
d
=
1
abcd=1
ab
c
d
=
1
. Prove that
a
2
+
b
2
+
c
2
+
d
2
+
a
b
+
a
c
+
a
d
+
b
c
+
b
d
+
d
c
≥
10
a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+dc \ge 10
a
2
+
b
2
+
c
2
+
d
2
+
ab
+
a
c
+
a
d
+
b
c
+
b
d
+
d
c
≥
10
Back to Problems
View on AoPS