MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia Regional
2022 Indonesia Regional
3
3
Part of
2022 Indonesia Regional
Problems
(1)
Not This Type of Inequality
Source: Indonesia RMO 2022, Essay No 3
8/24/2022
It is known that
x
x
x
and
y
y
y
are reals satisfying
5
x
2
+
4
x
y
+
11
y
2
=
3.
5x^2 + 4xy + 11y^2 = 3.
5
x
2
+
4
x
y
+
11
y
2
=
3.
Without using calculus (differentials/integrals), determine the maximum value of
x
y
ā
2
x
+
5
y
xy - 2x + 5y
x
y
ā
2
x
+
5
y
.
Indonesia
RMO
2022
algebra
inequalities