If three successive terms of a geometric sequence with ratio r correspond to the lengths of the three sides of a triangle, then determine whether or not [r]+[-r]=-1.

[x] is the greatest integer ≤ x.

If the triangle is equilateral, then r = 1 and [r]+[-r] = 0;

otherwise,

r != 1 and (-1+sqrt(5))/2 < r < (1+sqrt(5))/2 and [r]+[-r] = -1. 

Edited on March 19, 2007, 1:10 pm

Edited on March 19, 2007, 1:11 pm

Posted by Bractals on 2007-03-19 13:07:28