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National and Regional Contests
Bulgaria Contests
IFYM Int. Fest. of Young Mathematicians, Sozopol
2015 IFYM, Sozopol
3
inequality 1
inequality 1
Source:
April 3, 2011
inequalities
inequalities proposed
Problem Statement
Let
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
prove that:
a
3
(
a
+
b
)
3
+
b
3
(
b
+
c
)
3
+
c
3
(
c
+
a
)
3
≥
3
8
\frac{a^{3}}{(a+b)^{3}}+\frac{b^{3}}{(b+c)^{3}}+\frac{c^{3}}{(c+a)^{3}}\geq \frac{3}{8}
(
a
+
b
)
3
a
3
+
(
b
+
c
)
3
b
3
+
(
c
+
a
)
3
c
3
≥
8
3
Good luck! :D
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