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Junior Balkan MO
2014 Junior Balkan MO
3
JBMO 2014 #3 -- Inequality
JBMO 2014 #3 -- Inequality
Source:
June 23, 2014
inequalities
algebra
JBMO
High school olympiad
Problem Statement
For positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
a
b
c
=
1
abc=1
ab
c
=
1
prove that
(
a
+
1
b
)
2
+
(
b
+
1
c
)
2
+
(
c
+
1
a
)
2
≥
3
(
a
+
b
+
c
+
1
)
\left(a+\frac{1}{b}\right)^{2}+\left(b+\frac{1}{c}\right)^{2}+\left(c+\frac{1}{a}\right)^{2}\geq 3(a+b+c+1)
(
a
+
b
1
)
2
+
(
b
+
c
1
)
2
+
(
c
+
a
1
)
2
≥
3
(
a
+
b
+
c
+
1
)
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