a,b := (sqrt(108) +- 10)^(1/3) = (6*sqrt(3) +- 10)^(1/3), 0 < b < a One has a*b = (a^3*b^3)^(1/3) = 8^(1/3) = 2, which is elementary. Moreover a-b = a - 2/a is *guessed* to be 2 , using some calculator. The quadratic equation x - 2/x = 2 has solutions 1 +- sqrt(3), by hand. Taking 3rd powers one sees that a = 1 + sqrt(3). The assertion follows.

Date: Sun, 26 Jul 2020 14:55:27 -0700 From: Henry Baker <hbaker1@pipeline.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] High schoolers: simplify this expression Message-ID: <E1jzocv-0007m4-Tx@elasmtp-masked.atl.sa.earthlink.net> Content-Type: text/plain; charset="iso-8859-1"