Originally Posted by Chronos
OK, start from the first equation, a^2  b^2 = ab ± 1. Since a and b are both threedigit 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
