MathNet 2023-part-07 — 187 problems (EN–VI) Question 111

Let $x$, $y$, and $N$ be real numbers, with $y$ nonzero, such that the sets $\{(x+y)^2, (x-y)^2, x y, x / y\}$ and $\{4, 12.8, 28.8, N\}$ are equal. Compute the sum of the possible values of $N$.