VMO 1981 Problem 5

$x_1$, $x_2$, $x_3$, ... , $x_n$ are reals in the interval [a, b]. M = ($x_1$ + $x_2$ + ... + $x_n$)/n, V = ($x_1^2$ + $x_2^2$ + ... + $x_n^2$)/n. Show that $M^2$ ≥ 4Vab/(a + b)$^2$.