How to simplify ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) + (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2 to 2?
Subject: How to simplify ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) + (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2 to 2?
From: Andrej Vodopivec
Date: Tue, 14 Nov 2006 21:22:27 +0100
On 11/14/06, Humberto Bortolossi <humberto.bortolossi at gmail.com> wrote:
> Hi!
>
> Is there a way to make Maxima simplify the expression
>
> ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
> (2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2
>
> to 2?
(%i1) load(sqdnst)$
(%i2) ((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3))) +
(2-sqrt(3))/(sqrt(2)-sqrt(2-sqrt(3))))^2$
(%i3) ratsimp(scanmap(sqrtdenest, ratsimp(%)));
(%o3) 2
HTH,
Andrej