Potential energy as a function of r is given by U = A r ^ 10 - B r...

Given $U = \dfrac{A}{{r}^{10}} - \dfrac{B}{{r}^{5}}$.

Now, for equilibrium, $\dfrac{d U}{d r} = 0$.

So, differentiating the given equation,

$\dfrac{- 10A}{{r}^{11}} + \dfrac{5B}{{r}^{6}} = 0$

$⇒ \dfrac{10A}{{r}^{11}} = \dfrac{5B}{{r}^{6}} ⇒ {r}^{5} = \dfrac{2A}{B} ⇒ r = \left(\dfrac{2A}{B}\right)\dfrac{1}{5}$