Given real a1, a2, ..., an with arithmetic mean A and geometric mean G, show that

analysis/am.gm.bound New, unsolved

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Given real a1, a2, ..., an with arithmetic mean A and geometric mean G,
show that

                         [ sqrt(max(ai)) - sqrt(min(ai)) ]^2
              A - G  >=  -----------------------------------
                                         n

[ Editor: the ai must be non-negative for the geometric mean and the
square roots to make sense. ]

Show solution

No solution was found in the collected postings.

[ Editor: posed by Bill Taylor <wft@math.canterbury.ac.nz> as a
"chocolate fish" problem in sci.math and rec.puzzles, 28 Oct 1993. ]