MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2002 India IMO Training Camp
20
an easy cyclic inequality
an easy cyclic inequality
Source: India tst 2002 p20
June 30, 2012
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers. Prove that
a
b
+
b
c
+
c
a
≥
c
+
a
c
+
b
+
a
+
b
a
+
c
+
b
+
c
b
+
a
\frac{a}b+\frac{b}c+\frac{c}a \geq \frac{c+a}{c+b}+\frac{a+b}{a+c}+\frac{b+c}{b+a}
b
a
+
c
b
+
a
c
≥
c
+
b
c
+
a
+
a
+
c
a
+
b
+
b
+
a
b
+
c
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