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National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2007 Hanoi Open Mathematics Competitions
10
HOMC (Vietnam)
HOMC (Vietnam)
Source:
January 25, 2016
algebra
Problem Statement
Let a; b; c be positive real numbers such that
1
b
c
+
1
c
a
+
1
a
b
≥
1
\frac{1}{bc}+\frac{1}{ca}+\frac{1}{ab} \geq 1
b
c
1
+
c
a
1
+
ab
1
≥
1
. Prove that
a
b
c
+
b
c
a
+
c
a
b
≥
1
\frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab} \geq 1
b
c
a
+
c
a
b
+
ab
c
≥
1
.
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