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MathLinks Contest 1st
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0112 inequalities 1st edition Round 1 p2
0112 inequalities 1st edition Round 1 p2
Source:
May 9, 2021
inequalities
1st edition
Problem Statement
Prove that for all positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
the following inequality holds:
a
+
b
a
+
c
+
b
+
c
b
+
a
+
c
+
a
c
+
b
≤
a
b
+
b
c
+
c
a
\frac{a + b}{a + c}+\frac{b + c}{b + a}+\frac{c + a}{c + b} \le \frac{a}{b}+\frac{b}{c}+\frac{c}{a}
a
+
c
a
+
b
+
b
+
a
b
+
c
+
c
+
b
c
+
a
≤
b
a
+
c
b
+
a
c
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