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Very Easy Inequality - ILL 1970 Problem 1.
Very Easy Inequality - ILL 1970 Problem 1.
Source:
May 24, 2011
inequalities
Problem Statement
Prove that
a
b
a
+
b
+
b
c
b
+
c
+
c
a
c
+
a
≤
a
+
b
+
c
2
\frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ca}{c+a}\le \frac{a+b+c}{2}
a
+
b
ab
+
b
+
c
b
c
+
c
+
a
c
a
≤
2
a
+
b
+
c
, where
a
,
b
,
c
∈
R
+
a,b,c\in\mathbb{R}^{+}
a
,
b
,
c
∈
R
+
.
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