Problem

Source: Bolivia IMO TST 2022 Day 1 P1

Tags: Bolivia, algebra, TST, Gauss identity



Find all possible values of $\frac{1}{x}+\frac{1}{y}$, if $x,y$ are real numbers not equal to $0$ that satisfy $$x^3+y^3+3x^2y^2=x^3y^3$$