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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
9.4
2x2 x^4-2x^3+x=y^2-y , y^4-2y^3+y=x^2-x (III Soros Olympiad 1996-97 R1 9.4)
2x2 x^4-2x^3+x=y^2-y , y^4-2y^3+y=x^2-x (III Soros Olympiad 1996-97 R1 9.4)
Source:
May 29, 2024
algebra
system of equations
Problem Statement
Solve the system of equations
{
x
4
−
2
x
3
+
x
=
y
2
−
y
y
4
−
2
y
3
+
y
=
x
2
−
x
\begin{cases} x^4-2x^3+x=y^2-y \\ y^4-2y^3+y=x^2-x \end{cases}
{
x
4
−
2
x
3
+
x
=
y
2
−
y
y
4
−
2
y
3
+
y
=
x
2
−
x
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