Can X=2 and X=-2 at the same time?

[jgens]

so (sqrt 1 - sqrt 1) is different to
x=sqrt 1
x-x

No! Hopefully without confusing you too much, if we let $x = \sqrt{1}$ then $x=1$ because the $\sqrt$ operation retrieves the principal (positive) square root. However, if $x$ is a number such that $x^2 = 1$ then $x=1$ or $x=-1$. Now, using this second definition of $x$, once we choose a value for $x$ we need to stick with it. We can't have $x = 1$ and $x = -1$ at the same time because this would violate the law of non-contradiction and you're already assuming that $1 = -1$.

 

[The Chaz]

Stop feeding the troll (OP)!