A particle moves along a line joining two stationary masses, m₁ and m₂, which is separated by a fixed distance a. Let x denote the distance of the particle from m₁.
(a) Show that
x = Gm² / (x - a)² - Gm₁ / x²
where G is the gravitational constant.
(b) Find the particle's equilibrium position. Is it stable or unstable?