Clever Mathematician

Long ago, a clever mathematician used to cheat people. Once he borrowed
Rs.4000/- from a rich man. After a few days, he borrowed Rs.2000/- from
the same man. Many days passed, the mathematician did not return the money
to the rich man. The rich man went to the mathematician and asked to
return the money. But to his great surprise, the mathematician replied
that there is no need to pay the debt.

"See here, friend" said the mathematician " the sum of 4000 and 2000 is
equal to zero, so I do not have any balance to pay".

The rich man took the matter to the court. When the judge came to know
this, he was astonished. He asked the mathematician to prove that sum of
4000 and 2000 is zero, and not 6000.

The Clever mathematician agreed. He said:

let a = 4000, b = 2000 and c = 6000

a + b = c

Multiply both sides by a + b

(a + b) (a + b) = c (a + b)

a*a + ab + ba + b*b = ca + cb

a*a + ab - ca = cb - b*b - ba

a( a + b -c) = -b(b + a - c)

so a = - b

a + b = 0

Hence by putting the values of "a" and "b" as 4000 and 2000 respectively,
their sum is zero, so the mathematician saw no need to pay any money to
the rich man.

The above calculation has no doubt surprised you as it did the judge.

So, what do u say?