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Balkan MO Shortlist
2010 Balkan MO Shortlist
A3
Inequality1
Inequality1
Source:
November 30, 2010
inequalities
inequalities unsolved
Balkan
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be positive real numbers. Prove that
(
a
a
+
b
)
5
+
(
b
b
+
c
)
5
+
(
c
c
+
d
)
5
+
(
d
d
+
a
)
5
≥
1
8
(\frac{a}{a+b})^{5}+(\frac{b}{b+c})^{5}+(\frac{c}{c+d})^{5}+(\frac{d}{d+a})^{5}\ge \frac{1}{8}
(
a
+
b
a
)
5
+
(
b
+
c
b
)
5
+
(
c
+
d
c
)
5
+
(
d
+
a
d
)
5
≥
8
1
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