VMO 1980 Problem 2

Let $x_1$, $x_2$, ... , $x_n$ be positive reals with sum s. Show that ($x_1$ + $1/x_1$)$^2$ + ($x_2$ + $1/x_2$)$^2$ + ... + ($x_n$ + $1/x_n$)$^2$ ≥ n(n/s + s/n)$^2$.