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Mediterranean Mathematics Olympiad
2004 Mediterranean Mathematics Olympiad
3
Ab+bc+ca+2abc=1
Ab+bc+ca+2abc=1
Source: me but i do not know if it is true
March 16, 2006
trigonometry
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
and
a
b
+
b
c
+
c
a
+
2
a
b
c
=
1
ab+bc+ca+2abc=1
ab
+
b
c
+
c
a
+
2
ab
c
=
1
then prove that
2
(
a
+
b
+
c
)
+
1
≥
32
a
b
c
2(a+b+c)+1\geq 32abc
2
(
a
+
b
+
c
)
+
1
≥
32
ab
c
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