MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2014 Harvard-MIT Mathematics Tournament
16
2014 Guts #16: Maximum Given Constraint
2014 Guts #16: Maximum Given Constraint
Source:
April 20, 2014
Problem Statement
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
.
Back to Problems
View on AoPS