Clever Mathematician

Long ago, a 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 4000 + 2000 = 0............