MathDB
Problems
Contests
International Contests
Silk Road
2007 Silk Road
3
3
Part of
2007 Silk Road
Problems
(1)
Inequality
Source: SRMC 2007
8/7/2007
Find the max. value of
M
M
M
,such that for all
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
:
a
3
+
b
3
+
c
3
−
3
a
b
c
≥
M
(
∣
a
−
b
∣
3
+
∣
a
−
c
∣
3
+
∣
c
−
b
∣
3
)
a^{3}+b^{3}+c^{3}-3abc\geq M(|a-b|^{3}+|a-c|^{3}+|c-b|^{3})
a
3
+
b
3
+
c
3
−
3
ab
c
≥
M
(
∣
a
−
b
∣
3
+
∣
a
−
c
∣
3
+
∣
c
−
b
∣
3
)
inequalities
inequalities proposed