Mathematically Impossible..!!

[Referee-Observer]

a = b
a2 = ab = b2
a2 - b2 = a2 – ab
(a+b)(a-b) = a(a-b) so (a-b) on both sides cancel each other leaving
a+b = a
but a = b
a + a = a
2a = a
so 2 = 1
mathematically impossible..!!

[Baldric]

Whatever!

[Zacs-Master]

What about a2-a2 ?

[Buenchico]

I used to leave that written on a blackboard in my classroom and say nothing about it. It was interesting to see which pupils would be the first to read it and start asking questions. (Of course, 'divide by zero' errors can have more serious consequences. Do you remember the panic over 'Y2K Millennium Bug'?)

[emeritus]

http://mathforum.org/library/drmath/view/57116.html

[bhg481]

The flaw comes when you multiply anything by a-b . When a=b, a-b=0.

10*0 = 93*0 = anything else * 0.

[jim360]

My whole life is a lie.

This is one of those lovely "results" that's worth looking at now and again. Despite the fact that it's fairly well-known you'd be surprised how often similar errors are made, dividing by zero etc. Usually what happens is that alternative answers are missed, rather than the resulting answers are wrong, but still it's a mistake that's made too often.

[New Judge]

I'm sure you know that it falls apart at:

(a+b)(a-b) = a(a-b) so (a-b) on both sides cancel each other leaving
a+b = a

the "(a-b)" that you are cancelling out on both sides are actually different multiples of (a-b) and so do not cancel out at all.

[Referee-Observer]

Knew there was a catch, but unsure where, many thanks for all replies

[Noelieboy]

Fallacy!
(a+b)(a-b)= a(a-b)...correct so far - algebraically;
'so (a-b) on both sides cancel each other' is not true as, in mathematics, you may not divide by 0,
therefore, the result of 2=1 is not proven.

[razza]

zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz