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Junior Balkan MO
2016 Junior Balkan MO
2
JBMO 2016 Problem 2
JBMO 2016 Problem 2
Source:
June 26, 2016
inequalities
JBMO
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers.Prove that
8
(
a
+
b
)
2
+
4
a
b
c
+
8
(
b
+
c
)
2
+
4
a
b
c
+
8
(
a
+
c
)
2
+
4
a
b
c
+
a
2
+
b
2
+
c
2
≥
8
a
+
3
+
8
b
+
3
+
8
c
+
3
\frac{8}{(a+b)^2 + 4abc} + \frac{8}{(b+c)^2 + 4abc} + \frac{8}{(a+c)^2 + 4abc} + a^2 + b^2 + c ^2 \ge \frac{8}{a+3} + \frac{8}{b+3} + \frac{8}{c+3}
(
a
+
b
)
2
+
4
ab
c
8
+
(
b
+
c
)
2
+
4
ab
c
8
+
(
a
+
c
)
2
+
4
ab
c
8
+
a
2
+
b
2
+
c
2
≥
a
+
3
8
+
b
+
3
8
+
c
+
3
8
.
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