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2024 Bulgarian Winter Tournament
9.1
System of equations with two variables
System of equations with two variables
Source: Bulgarian Winter Tournament 2024 9.1
January 28, 2024
algebra
Problem Statement
Find all real
x
,
y
x, y
x
,
y
, satisfying
(
x
+
1
)
2
(
y
+
1
)
2
=
27
x
y
(x+1)^2(y+1)^2=27xy
(
x
+
1
)
2
(
y
+
1
)
2
=
27
x
y
and
(
x
2
+
1
)
(
y
2
+
1
)
=
10
x
y
.
(x^2+1)(y^2+1)=10xy.
(
x
2
+
1
)
(
y
2
+
1
)
=
10
x
y
.
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