Cancelling Squares: Can It Be Done?

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    Cancelling Squares
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SUMMARY

The discussion centers around the mathematical principle of cancelling squares in equations. Specifically, the equation (a-b)² = (c-b)² can lead to the conclusion that a = c or a = 2b - c, demonstrating that cancelling squares requires careful consideration of both positive and negative roots. The argument presented clarifies that while one can take the square root of both sides, it is crucial to acknowledge that this operation introduces two potential solutions. Thus, the assertion that squares can be cancelled without considering both cases is incorrect.

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

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