View Single Post
  #5  
Old 11-17-2019, 07:19 PM
Knowed Out's Avatar
Knowed Out is offline
Guest
 
Join Date: Nov 2001
Location: North Kakkalakee
Posts: 15,390
Quote:
Originally Posted by Chronos View Post
OK, start from the first equation, a^2 - b^2 = ab 1. Since a and b are both three-digit numbers, ab is going to be five to seven digits, meaning that that 1 is almost irrelevant. So to a very good approximation, a^2 - ab + b^2 = 0. Defining x == a/b, this means that x^2 - x - 1 ~= 0, or x ~= (1+sqrt(5))/2 ~= 1.61803
The first equation is a2 - b2 = ab 1, but when you shifted ab over, shouldn't the result be a2 - ab - b2 ~= 0?

Also, if you're defining x == a/b, wouldn't the the result be b2x2 - ab - a2/x2 ~= 0? How did you get x2 - x -1 ~= 0? Moreover, how did you leap to x ~= (1+sqrt(5))/2?