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Junior Balkan MO
2011 Junior Balkan MO
1
Jbmo 2011 Problem 1
Jbmo 2011 Problem 1
Source: Jbmo
June 21, 2011
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
a
b
c
=
1
abc = 1
ab
c
=
1
. Prove that:
∏
(
a
5
+
a
4
+
a
3
+
a
2
+
a
+
1
)
≥
8
(
a
2
+
a
+
1
)
(
b
2
+
b
+
1
)
(
c
2
+
c
+
1
)
\displaystyle\prod(a^5+a^4+a^3+a^2+a+1)\geq 8(a^2+a+1)(b^2+b+1)(c^2+c+1)
∏
(
a
5
+
a
4
+
a
3
+
a
2
+
a
+
1
)
≥
8
(
a
2
+
a
+
1
)
(
b
2
+
b
+
1
)
(
c
2
+
c
+
1
)
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