MathDB
The "strange mean"

Source: Kürschák 1992, problem 1

July 20, 2014
inequalities proposedinequalities

Problem Statement

Define for nn given positive reals the strange mean as the sum of the squares of these numbers divided by their sum. Decide which of the following statements hold for n=2n=2:
a) The strange mean is never smaller than the third power mean.
b) The strange mean is never larger than the third power mean.
c) The strange mean, depending on the given numbers, can be larger or smaller than the third power mean.
Which statement is valid for n=3n=3?
Back to ProblemsView on AoPS