1=2

[PhoenixOfPanem]

a = b (initial supposition)
ab = b^2 (multiply both sides by b)
ab-a^2 = b^2-a^2 (subtract a^2 from both sides)
a(b-a) = b^2-a^2 (factor out a from the left side using distributive property)
a(b-a) = (b-a)(b+a) (factor the right side using difference of squares)
a = b+a (cancel both b-a terms by dividing both sides by it)
a = a+a (substitute a for b, legal since a=b)
a = 2a (simplify)
1 = 2 (divide both sides by a)

http://www.youtube.com/watch?v=iceFDrhK73U


...What's wrong with this answer?

[Camaclue]

you're silly and nobody loves me

[Shadow]

a(b-a) = (b-a)(b+a) (factor the right side using difference of squares)
a = b+a (cancel both b-a terms by dividing both sides by it)

This is the problem. Since b=a, you can't cancel b-a because that would be dividing by 0. At this point, the equation just reads 0=0 and there's nothing more you can do with it.

Also, even if you got to this point legally (which you didn't)
a = 2a (simplify)
Then this implies that a=0, not that 1=2.

The person in the youtube video is an idiot.

[PhoenixOfPanem]

you're silly and nobody cares

Thank you very little.

a(b-a) = (b-a)(b+a) (factor the right side using difference of squares)
a = b+a (cancel both b-a terms by dividing both sides by it)

This is the problem. Since b=a, you can't cancel b-a because that would be dividing by 0. At this point, the equation just reads 0=0 and there's nothing more you can do with it.

Exactly. I did that problem a few months ago and just wanted to see if anyone else figured it out. :)

[Camaclue]

I read about this one about a guy buying a thing and he borrows money from some people and there's a missing dollar.

[Wordsarecool]

Keep your maths numbers math away from me!!!!