Let a, b, and c be nonnegative numbers. Follow steps (a) through (e) to show that...

Let a, b, and c be nonnegative numbers. Follow steps (a) through (e) to show that

with equality holding if and only if a = b = c. This result is known as the arithmetic-geometric mean inequality for three numbers. (Applications are developed in the projects at the ends of Sections 4.6 and 4.7.) (a) By multiplying out the right-hand side, show that the following equation holds for all real numbers A, B, and C.

(b) Now assume for the remainder of this exercise that A, B, and C are nonnegative numbers. Use equation (1) to explain why