Problems(1)
Curves A,B,C and D are defined in the plane as follows:
\begin{align*}
A &= \left\{ (x,y): x^2-y^2 = \frac{x}{x^2+y^2} \right\}, \\
B &= \left\{ (x,y): 2xy + \frac{y}{x^2+y^2} = 3 \right\}, \\
C &= \left\{ (x,y): x^3-3xy^2+3y=1 \right\}, \\
D &= \left\{ (x,y): 3x^2 y - 3x - y^3 = 0\right\}.
\end{align*}
Prove that A∩B=C∩D. Putnam