40. (a) Show that for any positive numbers and , the geometric mean is less than the arithmetic mean,⁵ except when ; in that case, the two means are equal. (Hint: Show that the triangle in Figure 14.2 is a right triangle.)

(b) If is a number such that the Webster and Hill-Huntington roundings of differ, show that is greater than the Hill-Huntington rounding point and is less than the Webster rounding point . Conclude that, in this case, the Hill-Huntington rounding of is equal to and the Webster rounding is equal to .

(c) Explain why the fact established in part (b) implies that the Hill-Huntington method is more favorable to small states than the Webster method.