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Further Geometric Numbers (2) (Posted on 2007-03-19) Difficulty: 1 of 5
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.

See The Solution Submitted by K Sengupta    
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Solution Solution | Comment 3 of 4 |
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

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