MathNet 2016-part-03 — 184 problems (EN–VI) Question 115

Let $x$ and $y$ be real nonzero numbers, such that $x^3 + y^3 + 3x^2y^2 = x^3y^3$. Determine the set of the possible values of $E = \frac{1}{x} + \frac{1}{y}$.