Solved: Geometric and arithmetic means Given positive
Chapter 12, Problem 60(choose chapter or problem)
Geometric and arithmetic means Given positive numbers x1, c, xn, prove that the geometric mean 1x1x2 gxn21>n is no greater than the arithmetic mean 1x1 + g+ xn2>n in the following cases. a. Find the maximum value of xyz, subject to x + y + z = k, where k is a real number and x 7 0, y 7 0, and z 7 0. Use the result to prove that 1xyz21>3 x + y + z 3 . b. Generalize part (a) and show that 1x1x2gxn21>n x1 + g+ xn n .
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