An algebra problem by A Former Brilliant Member
A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?"
After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers."
The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?
The answer is 32.
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1 solution
it is that simple . .as the merchant divides the coins in two unequal parts let them be x and y . . .now as per the statement . . . 32 times the difference b/w the no. is equal to the difference b/w the square of the two number now the eq follows . . . . .let the difference be x-y . . . .now it would be . . . 32(x-y) =x^2 - y^2 32(x-y) = (x-y)(x+y) i.e. (x+y) = 32