The arithmetic mean of two numbers a and b is defined as (a+b)/2; the geometric mean of
Chapter 4, Problem 47(choose chapter or problem)
The arithmetic mean of two numbers a and b is defined as (a+b)/2; the geometric mean of two positive numbers a and b is defined as ab. (a) For two positive numbers, which of the two means is larger? Justify your answer. [Hint: Define f(x)=(a+x)/2ax for fixed a.] (b) For three positive numbers a, b, c, the arithmetic and geometric mean are (a+b+c)/3 and 3 abc, respectively. Which of the two means of three numbers is larger? [Hint: Redefine f(x) for fixed a and b.]
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