MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2005 Iran MO (3rd Round)
5
a,b,c
a,b,c
Source: Iran 2005
August 27, 2005
trigonometry
geometry
inequalities
inequalities proposed
Problem Statement
Suppose
a
,
b
,
c
∈
R
+
a,b,c \in \mathbb R^+
a
,
b
,
c
∈
R
+
and
1
a
2
+
1
+
1
b
2
+
1
+
1
c
2
+
1
=
2
\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}=2
a
2
+
1
1
+
b
2
+
1
1
+
c
2
+
1
1
=
2
Prove that
a
b
+
a
c
+
b
c
≤
3
2
ab+ac+bc\leq \frac32
ab
+
a
c
+
b
c
≤
2
3
Back to Problems
View on AoPS