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Balkan MO
2005 Balkan MO
3
Balkan 2005-3
Balkan 2005-3
Source:
May 6, 2005
inequalities
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Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers. Prove the inequality
a
2
b
+
b
2
c
+
c
2
a
≥
a
+
b
+
c
+
4
(
a
−
b
)
2
a
+
b
+
c
.
\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\geq a+b+c+\frac{4(a-b)^2}{a+b+c}.
b
a
2
+
c
b
2
+
a
c
2
≥
a
+
b
+
c
+
a
+
b
+
c
4
(
a
−
b
)
2
.
When does equality occur?
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