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International Contests
Silk Road
2006 Silk Road
2
International competition SRMC 2006 P-2
International competition SRMC 2006 P-2
Source:
September 8, 2010
inequalities
inequalities proposed
Problem Statement
For positive
a
,
b
,
c
a,b,c
a
,
b
,
c
, such that
a
b
c
=
1
abc=1
ab
c
=
1
prove the inequality:
4
(
a
b
3
+
b
c
3
+
c
a
3
)
≤
3
(
2
+
a
+
b
+
c
+
1
a
+
1
b
+
1
c
)
2
3
4(\sqrt[3]{\frac{a}{b}}+\sqrt[3]{\frac{b}{c}}+\sqrt[3]{\frac{c}{a}}) \leq 3(2+a+b+c+\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})^{\frac{2}{3}}
4
(
3
b
a
+
3
c
b
+
3
a
c
)
≤
3
(
2
+
a
+
b
+
c
+
a
1
+
b
1
+
c
1
)
3
2
.
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