Greetings friends, I have come across an argument on cancelling the squares on either side of an equation. For example if the equation is (a-b)^2=(c-b)^2 my argument is that i can cancel the squares by taking the square root of both sides as to get (a-b)=(c-b) and hence a=c. But others says that squares cannot be remove as such. So I thought i would consult you guys. What do you think, am i wrong or are they wrong? thanx for your help!
A^2=B^2 then that tells us that A^2-B^2 = 0, or that (A-B)(A+B) = 0, and so we have that either A=B, or A=-B. This is rather evident since, consider that (-2)^2=2^2.