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Austria Contests
Austrian MO Regional Competition
1970 Regional Competition For Advanced Students
4
4
Part of
1970 Regional Competition For Advanced Students
Problems
(1)
Find real solutions to set of equations
Source: AustriaMO1970 problem 4
6/29/2011
Find all real solutions of the following set of equations:
72
x
3
+
4
x
y
2
=
11
y
3
72x^3+4xy^2=11y^3
72
x
3
+
4
x
y
2
=
11
y
3
27
x
5
−
45
x
4
y
−
10
x
2
y
3
=
−
143
32
y
5
27x^5-45x^4y-10x^2y^3=\frac{-143}{32}y^5
27
x
5
−
45
x
4
y
−
10
x
2
y
3
=
32
−
143
y
5
number theory
greatest common divisor
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