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2014 Harvard-MIT Mathematics Tournament
16
16
Part of
2014 Harvard-MIT Mathematics Tournament
Problems
(1)
2014 Guts #16: Maximum Given Constraint
Source:
4/20/2014
Suppose that
x
x
x
and
y
y
y
are positive real numbers such that
x
2
ā
x
y
+
2
y
2
=
8
x^2-xy+2y^2=8
x
2
ā
x
y
+
2
y
2
=
8
. Find the maximum possible value of
x
2
+
x
y
+
2
y
2
x^2+xy+2y^2
x
2
+
x
y
+
2
y
2
.