MathDB
Problems
Contests
National and Regional Contests
Bulgaria Contests
Bulgaria National Olympiad
1980 Bulgaria National Olympiad
Problem 4
Might be well-known...
Might be well-known...
Source:
August 29, 2017
inequalities
inequalities open
Inequality
Problem Statement
Let
a
a
a
,
b
b
b
, and
c
c
c
be non-negative reals. Prove that
a
3
+
b
3
+
c
3
+
6
a
b
c
≥
(
a
+
b
+
c
)
3
4
a^3+b^3+c^3+6abc\ge \frac{(a+b+c)^3}{4}
a
3
+
b
3
+
c
3
+
6
ab
c
≥
4
(
a
+
b
+
c
)
3
.
Back to Problems
View on AoPS