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Greece Contests
Greece National Olympiad
2011 Greece National Olympiad
3
3
Part of
2011 Greece National Olympiad
Problems
(1)
Inequality from Greece
Source: Greek Mathematical Olympiad 2011 - P3
5/13/2011
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive real numbers with sum
6
6
6
. Find the maximum value of
S
=
a
2
+
2
b
c
3
+
b
2
+
2
c
a
3
+
c
2
+
2
a
b
3
.
S = \sqrt[3]{{{a^2} + 2bc}} + \sqrt[3]{{{b^2} + 2ca}} + \sqrt[3]{{{c^2} + 2ab}}.
S
=
3
a
2
+
2
b
c
+
3
b
2
+
2
c
a
+
3
c
2
+
2
ab
.
inequalities
inequalities unsolved