MathDB
Problems
Contests
International Contests
Silk Road
2014 Silk Road
3
3
Part of
2014 Silk Road
Problems
(1)
Inequality from SRMC
Source: SRMC 2014
4/1/2014
a
,
b
,
c
≥
0
,
a
3
+
b
3
+
c
3
+
a
b
c
=
4
a,b,c\ge 0,\ \ \ a^3+b^3+c^3+abc=4
a
,
b
,
c
≥
0
,
a
3
+
b
3
+
c
3
+
ab
c
=
4
Prove that
a
3
b
+
b
3
c
+
c
3
b
≤
3
a^3b+b^3c+c^3b \le 3
a
3
b
+
b
3
c
+
c
3
b
≤
3
inequalities
inequalities proposed