There is a question that asks: Find three consecutive integers such that the sum of their squares is 149?
I chose to represent the consecutive integers as x, x+1, x+2. Another person chose to represent it as x-1, x, x+1. It then becomes:
x^2 + (x+1)^2 + (x+2)^2 = 149
(x-1)^2 + (x)^2 + (X+2)^2 = 149
The second method gave 7 or -7 as an answer which does give 149. However, when I plug 7 into my method, it does not work. Why? Is it because my method will find a different 3 consecutive integer that will work?