Question 48
We call an ordered pair $(x, y)$ of real numbers *auroral* if the equations $x = y(3 - y)^2$ and $y = x(3 - x)^2$ hold simultaneously.
Find all integers $k$ for which there exists an auroral pair $(x, y)$ of real numbers with $x + y = k$.
Find all integers $k$ for which there exists an auroral pair $(x, y)$ of real numbers with $x + y = k$.