1=12=(-1)2=√1, yes? Are we all familiar with that? (What? You're not? Oh, go take a math class.)
Therefore:
√12=√(-1)2
=1 =-1 (since square roots always cancel out square powers)
Therefore 1=-1 and 2=0 (adding 1 to both sides).
So what's the problem? Well, the problem is: square roots do not cancel out square powers, although they certainly appear to. Ever heard of BODMAS or PEMDAS? Same thing, different acronym. Evaluate 12 or (-1)2 first, then find the root of the answer. It ends up coming out to 1 both times.
Also: ever heard of the modulus or piecewise function? It's defined as √x2 or |x|, and its graph looks like
y
\ | /
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\|/
---------------------x
|
|
Note that y=x looks like:
y
| /
| /
| /
| /
| /
| /
| /
| /
|/
---------------------x
/|
/ |
/ |
/ |
/ |
and nothing like our friend |x|.
God, I love proving stuff.