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Problems
Contests
National and Regional Contests
Taiwan Contests
Taiwan National Olympiad
2006 Taiwan National Olympiad
1
Symmetric
Symmetric
Source: Taiwan NMO 2006
March 21, 2006
inequalities
inequalities proposed
Problem Statement
Positive reals
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfy
a
b
c
=
1
abc=1
ab
c
=
1
. Prove that
1
+
3
a
+
b
+
c
≥
6
a
b
+
b
c
+
c
a
\displaystyle 1+ \frac{3}{a+b+c} \ge \frac{6}{ab+bc+ca}
1
+
a
+
b
+
c
3
≥
ab
+
b
c
+
c
a
6
.
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