Putnam 2001 B2
Source:
February 27, 2012
PutnamUSAMTSalgebrasystem of equationscollege contests
Problem Statement
Find all pairs of real numbers satisfying the system of equations:
\begin{align*}\frac{1}{x} + \frac{1}{2y} &= (x^2+3y^2)(3x^2+y^2)\\
\frac{1}{x} - \frac{1}{2y} &= 2(y^4-x^4)\end{align*}