Really? What if the poster had posted ??

After squaring.....Voila! the same equation!!

So what is the reason?

You have introduced an additional solution by squaring!

Now ,

So generally we choose an x such that x > y and claim x^2 > y^2(implicitly assuming x and y are positive)

In topsquarks problem, we implicitly assumed (x-2) is positive while doing manipulations. So the final solution is .