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Flanders Junior Olympiad
2002 Flanders Junior Olympiad
1
inequality - well known
inequality - well known
Source: flanders '02
September 28, 2005
inequalities
Junior
algebra
Problem Statement
Prove that for all
a
,
b
,
c
∈
R
0
+
a,b,c \in \mathbb{R}^+_0
a
,
b
,
c
∈
R
0
+
we have
a
b
c
+
b
a
c
+
c
a
b
≥
2
a
+
2
b
−
2
c
\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab} \ge \frac2a+\frac2b-\frac2c
b
c
a
+
a
c
b
+
ab
c
≥
a
2
+
b
2
−
c
2
and determine when equality occurs.
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