VMO 1981 Problem 2

Let $p, q$ be real numbers with $0 < p < q$ and let $t_1, t_2, \cdots, t_n$ be real numbers in the interval $[p, q]$ . Denote by $A$ and $B$ the arithmetic means of $t_1, t_2, \cdots, t_n$ and of $t_1^2, t_2^2,\cdots , t_n^2$ , respectively. Prove that $$\frac{A^2}{B}\ge\frac{4pq}{(p + q)^2}.$$