a=b
a^2=ab
a^2+b^2=ab-b^2
(a-b)(a+b)=b(a-b)
a+b=b
b
2=1

why is this proof wrong?

Leah

Hi Leah

There is an error in your supposed proof. I think it should be

	a = b
	a2 = ab	(Multiply both sides by a.)
	a2 - b2 = ab - b2	(Subtract b2 from both sides.)
	(a + b)(a - b) = b(a - b)	(Factor.)
	a + b = b	(Cancel.)
But a = b and so,
	2a = a	(Replace b by a.)
and thus
	2 = 1	(Cancel.)

The place to look for a flaw is any place where you cancel. Since cancellation is actually division you need to check each place where you cancel be sure that you are not dividing by zero. Another way to look for the flaw is to use a specific value. Since the proof is supposedly true for any values of a and b as long as a = b, take a specific value, say a = b = 5 and trace through the steps to see where the flaw is.

Cheers
Penny