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2005 German National Olympiad
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Source: DeMO 2005, classes 11 and 12/13, 1st day, problem 1
5/9/2005
Find all pairs (x; y) of real numbers satisfying the system of equations
x
3
+
1
−
x
y
2
−
y
2
=
0
x^3 + 1 - xy^2 - y^2 = 0
x
3
+
1
−
x
y
2
−
y
2
=
0
;
y
3
−
1
−
x
2
y
+
x
2
=
0
y^3 - 1 - x^2y + x^2 = 0
y
3
−
1
−
x
2
y
+
x
2
=
0
. Darij
algebra
system of equations