MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2015 Hanoi Open Mathematics Competitions
13
(x^2 + y^2 - 2) (x + y)^2 +(xy + 1)^2 = 0, rational (HOMC 2015 J Q13)
(x^2 + y^2 - 2) (x + y)^2 +(xy + 1)^2 = 0, rational (HOMC 2015 J Q13)
Source:
August 6, 2019
algebra
rational
equation
Problem Statement
Give rational numbers
x
,
y
x, y
x
,
y
such that
(
x
2
+
y
2
−
2
)
(
x
+
y
)
2
+
(
x
y
+
1
)
2
=
0
(x^2 + y^2 - 2) (x + y)^2 + (xy + 1)^2 = 0
(
x
2
+
y
2
−
2
)
(
x
+
y
)
2
+
(
x
y
+
1
)
2
=
0
Prove that
1
+
x
y
\sqrt{1 + xy}
1
+
x
y
is a rational number.
Back to Problems
View on AoPS