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National and Regional Contests
Poland Contests
Poland - Second Round
2005 Poland - Second Round
3
Poland 2005
Poland 2005
Source:
November 17, 2010
convex-concave inequalities
algebra
Poland
inequalities
inequalities proposed
Problem Statement
Prove that if the real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
lie in the interval
[
0
,
1
]
[0,1]
[
0
,
1
]
, then
a
b
c
+
1
+
b
a
c
+
1
+
c
a
b
+
1
≤
2
\frac{a}{bc+1}+\frac{b}{ac+1}+\frac{c}{ab+1}\le 2
b
c
+
1
a
+
a
c
+
1
b
+
ab
+
1
c
≤
2
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