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Balkan MO Shortlist
2012 Balkan MO Shortlist
A6
A6
Part of
2012 Balkan MO Shortlist
Problems
(1)
Maximum value of cyclic expression
Source: Romania TST 2 2012, Problem 4
5/10/2012
Let
k
k
k
be a positive integer. Find the maximum value of
a
3
k
−
1
b
+
b
3
k
−
1
c
+
c
3
k
−
1
a
+
k
2
a
k
b
k
c
k
,
a^{3k-1}b+b^{3k-1}c+c^{3k-1}a+k^2a^kb^kc^k,
a
3
k
−
1
b
+
b
3
k
−
1
c
+
c
3
k
−
1
a
+
k
2
a
k
b
k
c
k
,
where
a
a
a
,
b
b
b
,
c
c
c
are non-negative reals such that
a
+
b
+
c
=
3
k
a+b+c=3k
a
+
b
+
c
=
3
k
.
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