Suppose x1,...,xn and y1,...,yn are real numbers, with x = y = 0 and sx = sy = 1. Show that 1 n

n i=1(xi + yi)2 = 2(1 + r) and 1

n

n i=1(xi − yi)2 = 2(1 − r), where r = r(x, y). Show that

−1 ≤ r ≤ 1.