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2024 Chile National Olympiad.
4
Circle is the solution????
Circle is the solution????
Source:
October 23, 2024
algebra
Chile
Problem Statement
Find all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of real numbers that satisfy the system
(
x
+
1
)
(
x
2
+
1
)
=
y
3
+
1
(x + 1)(x^2 + 1) = y^3 + 1
(
x
+
1
)
(
x
2
+
1
)
=
y
3
+
1
(
y
+
1
)
(
y
2
+
1
)
=
x
3
+
1
(y + 1)(y^2 + 1) = x^3 + 1
(
y
+
1
)
(
y
2
+
1
)
=
x
3
+
1
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