MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2010 Saint Petersburg Mathematical Olympiad
6
Inequality
Inequality
Source: St Petersburg Olympiad 2010, Grade 11, P6
September 14, 2017
algebra
Inequality
Problem Statement
For positive numbers is true that
a
b
+
a
c
+
b
c
=
a
+
b
+
c
ab+ac+bc=a+b+c
ab
+
a
c
+
b
c
=
a
+
b
+
c
Prove
a
+
b
+
c
+
1
≥
4
a
b
c
a+b+c+1 \geq 4abc
a
+
b
+
c
+
1
≥
4
ab
c
Back to Problems
View on AoPS