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Eotvos Mathematical Competition (Hungary)
1896 Eotvos Mathematical Competition
2
Prove that the equations $$x^2-3xy+2y^2+x-y=0 \text{ and } x^2-2xy+y^2-5x+7y=0$$
Prove that the equations $$x^2-3xy+2y^2+x-y=0 \text{ and } x^2-2xy+y^2-5x+7y=0$$
Source: Eotvos 1896 p2
March 14, 2020
algebra
Problem Statement
Prove that the equations
x
2
−
3
x
y
+
2
y
2
+
x
−
y
=
0
and
x
2
−
2
x
y
+
y
2
−
5
x
+
7
y
=
0
x^2-3xy+2y^2+x-y=0 \text{ and } x^2-2xy+y^2-5x+7y=0
x
2
−
3
x
y
+
2
y
2
+
x
−
y
=
0
and
x
2
−
2
x
y
+
y
2
−
5
x
+
7
y
=
0
imply the equation
x
y
−
12
x
+
15
y
=
0
xy-12x+15y=0
x
y
−
12
x
+
15
y
=
0
.
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