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National and Regional Contests
Morocco Contests
Morocco National Olympiad
2011 Morocco National Olympiad
2
Moroccan MO
Moroccan MO
Source:
April 30, 2011
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be three postive real numbers such that
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Prove that
9
a
b
c
≤
a
b
+
a
c
+
b
c
<
1
/
4
+
3
a
b
c
9abc\leq ab+ac+bc < 1/4 +3abc
9
ab
c
≤
ab
+
a
c
+
b
c
<
1/4
+
3
ab
c
.
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