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2010 China Northern MO
5
China Northern Mathematical Olympiad 2010 , Problem 5
China Northern Mathematical Olympiad 2010 , Problem 5
Source:
October 2, 2014
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers such that
(
a
+
2
b
)
(
b
+
2
c
)
=
9
(a+2b)(b+2c)=9
(
a
+
2
b
)
(
b
+
2
c
)
=
9
. Prove that
a
2
+
b
2
2
+
2
b
3
+
c
3
2
3
≥
3.
\sqrt{\frac{a^2+b^2}{2}}+2\sqrt[3]{\frac{b^3+c^3}{2}}\geq 3.
2
a
2
+
b
2
+
2
3
2
b
3
+
c
3
≥
3.
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