can anyone explain this amazing mathematical puzzle?

Question

let
a=4000
b=2000
a+b=c where c is the total cost

multiply (a+b) in both sides
(a+b)(a+b)=c(a+b)
aa+ab+ab+bb=ca+cb
aa+ab-ca=cb-ab-bb
aa+ab-ca= -ab-bb+cb
a(a+b-c)=-b(a+b-c)
a=-b
a+b=0
!!!!!!!!!!!

but i thought 4000+2000 was 6000?!?!?!?!?!

can anyone explain this to me???

all you guys are really good!!

Answer 1

a+b-c=0
Division by a+b-c is division by zero, an "illegal" operation.

I think that the "proof" is saying that the only way to make the process true is if a+b=0. The "proof" stands apart from the assignment of values (a=4000, b=6000).

Answer 2

Since a+b=c, then a+b-c = 0
You therefor divided by zero in the second to the last step
As you know, division by zero is a big fat no-no.
Your conclusion that a+b =0 is therefore wrong.

Answer 3

easy ;-)

you divide by (a+b-c), whereas you start by saying that a+b=c. So you divide by 0, so the division operation breaks down, so anything after that step becomes meaningless, in this case when you say a=-b

Answer 4

Ha! a+b-c = 0 so you have zero=zero as for dividing by zero don't even try that.

Answer 5

a+b-c = 0, and so you divide by zero in the step which gets you to a=-b

you can't divide by zero, so that step invalidates the process

Answer 6

To get from

a(a+b-c)=-b(a+b-c) to a = -b, you must divide by (a+b-c), which is equal to zero. This is one reason why dividing by zero is a no-no.