RU-ALLRUSSIAN 1978 Problem 13

a and b are positive real numbers. $\mathbf{x}_i$ are real numbers lying between a and b. Show that $(\mathbf{x}_1 + \mathbf{x}_2 + \ldots + \mathbf{x}_n)(1 / \mathbf{x}_1 + 1 / \mathbf{x}_2 + \ldots + 1 / \mathbf{x}_n)\leq \mathrm{n}^2 (\mathrm{a} + \mathrm{b})^2 /4\mathrm{ab}$ .