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2015 AIME Problems
14
Polynomial Given Values Find Value of Another Polynomial
Polynomial Given Values Find Value of Another Polynomial
Source: 2015 AIME 2 Problem 14
March 26, 2015
algebra
polynomial
Problem Statement
Let
x
x
x
and
y
y
y
be real numbers satisfying
x
4
y
5
+
y
4
x
5
=
810
x^4y^5+y^4x^5=810
x
4
y
5
+
y
4
x
5
=
810
and
x
3
y
6
+
y
3
x
6
=
945
x^3y^6+y^3x^6=945
x
3
y
6
+
y
3
x
6
=
945
. Evaluate
2
x
3
+
(
x
y
)
3
+
2
y
3
2x^3+(xy)^3+2y^3
2
x
3
+
(
x
y
)
3
+
2
y
3
.
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