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India Pre-Regional Mathematical Olympiad
2016 India PRMO
11
2016 preRMO p11, M is max of (x^4y+x^3y+x^2y+xy+xy^2+xy^3+xy^4) if x+y=3
2016 preRMO p11, M is max of (x^4y+x^3y+x^2y+xy+xy^2+xy^3+xy^4) if x+y=3
Source:
August 9, 2019
algebra
maximum
floor function
Problem Statement
For real numbers
x
x
x
and
y
y
y
, let
M
M
M
be the maximum value of the expression
x
4
y
+
x
3
y
+
x
2
y
+
x
y
+
x
y
2
+
x
y
3
+
x
y
4
x^4y + x^3y + x^2y + xy + xy^2 + xy^3 + xy^4
x
4
y
+
x
3
y
+
x
2
y
+
x
y
+
x
y
2
+
x
y
3
+
x
y
4
, subject to
x
+
y
=
3
x + y = 3
x
+
y
=
3
. Find
[
M
]
[M]
[
M
]
.
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