Cancelling Squares: Can It Be Done?

[PhYsIcAlLy QuAnTuM]

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!

 

[robert Ihnot]

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.

 

[HallsofIvy]

In other words, if (a-b)^2= (c-d)^2 then EITHER a-b= c-d OR a-b= d-c.