MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2015 ASDAN Math Tournament
9
2015 Algebra #9
2015 Algebra #9
Source:
July 1, 2022
2015
Algebra Test
Problem Statement
Compute all pairs of nonzero real numbers
(
x
,
y
)
(x,y)
(
x
,
y
)
such that
x
x
2
+
y
+
y
x
+
y
2
=
−
1
and
1
x
+
1
y
=
1.
\frac{x}{x^2+y}+\frac{y}{x+y^2}=-1\qquad\text{and}\qquad\frac{1}{x}+\frac{1}{y}=1.
x
2
+
y
x
+
x
+
y
2
y
=
−
1
and
x
1
+
y
1
=
1.
Back to Problems
View on AoPS