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2009 District Olympiad
1
x^2y^2 + 1 = x^2 + xy 3x3 system 2009 Romania District VIII p1
x^2y^2 + 1 = x^2 + xy 3x3 system 2009 Romania District VIII p1
Source:
August 16, 2024
algebra
system of equations
Problem Statement
Find all non-negative real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
satisfying
x
2
y
2
+
1
=
x
2
+
x
y
x^2y^2 + 1 = x^2 + xy
x
2
y
2
+
1
=
x
2
+
x
y
,
y
2
z
2
+
1
=
y
2
+
y
z
y^2z^2 + 1 = y^2 + yz
y
2
z
2
+
1
=
y
2
+
yz
and
z
2
x
2
+
1
=
z
2
+
x
z
z^2x^2 + 1 = z^2 + xz
z
2
x
2
+
1
=
z
2
+
x
z
.
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