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Gulf Math Olympiad
2012 Gulf Math Olympiad
2
2
Part of
2012 Gulf Math Olympiad
Problems
(1)
An inequality
Source: Gulf MO 2012, Problem 2
6/14/2012
Prove that if
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive real numbers, then the least possible value of
6
a
3
+
9
b
3
+
32
c
3
+
1
4
a
b
c
6a^3 + 9b^3 + 32c^3 + \frac{1}{4abc}
6
a
3
+
9
b
3
+
32
c
3
+
4
ab
c
1
is
6
6
6
. For which values of
a
,
b
a, b
a
,
b
and
c
c
c
is equality attained?
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