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Mathematician

Long ago, a mathematician used to cheat people. Oncehe borrowedRs.4000/- from a rich man. After a few days, heborrowed Rs.2000/- from the same man.
Many days passed, the mathematician did not return themoney to the rich man. The rich man went to themathematician and asked to return the money.
But to his great surprise, the mathematician replied that there is noneed to pay the debt.
"See here, friend" said the mathematician " the sum of4000 and 2000 is equal tozero, so I do not have any balance to pay".
The rich man took the matter to the court. When the judge came to knowthis, he was astonished. He asked the mathematician toprove 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