The product of three consecutive numbers when divided by each of them in turn gives three quotients. The sum of these three quotients is equal to 74.

What are the numbers ?

Let the 3 numbers be x-1 , x & x+1

So we have:

(x-1) (x) (x+1) / (x-1) = (x) (x+1) = x^2 + x
(x-1) (x) (x+1) / (x) = (x-1) (x+1) = x^2 - 1
(x-1) (x) (x+1) / (x+1) = (x-1) (x) = x^2 - x

Adding all the quotients we get:

x^2 + x + x^2 - 1 + x^2 - x = 74
3x^2 - 1 = 74
x^2 = 25
x = 5 or -5

So the numbers are 4,5,6 or -4,-5,-6.

Posted by Syzygy on 2005-01-21 12:10:12