An object of mass m is confined to move along the x-axis in a one-dimensional system. The particle experiences a  potential energy function given by U(x) = A/x³ - B/x² where A and B are constants (always positive). Determine the equilibrium positions of the particle where the net force on the particle is zero.

Hint: Recall that the net force acting on the particle is the negative gradient of the potential energy function.