Question

The product of 3 consecutive nos when divided by each of them in turn the sum of the 3 quotient is 74. Find the nos

Answer 1

Suppose the three consecutive numbers are x; (x+1) and (x+2).

Product of these numbers = x(x+1)

(x+2) = x(x2+3x+2) = x3+3x2+2x

Three quotients are given by;

(x+1)(x+2); when divided by x.x

(x+2); when divided by (x+1).x

(x+1); when divided by (x+2).

Now according to the question we have;

(x+1)(x+2)+x(x+2)+x(x+1) = 74⇒(x2+3x+2)

+(x2+2x)+(x2+x) = 74⇒3x2+6x+2 = 74⇒3x2+6

x−72 = 0⇒x2+2x−24 = 0⇒x2+6x−4

x−24 = 0⇒x(x+6)−4(x+6) = 0⇒(x−4)

(x+6) = 0⇒x = 4 and x = −6

So three consecutive numbers are either 4, 5 and 6 or -6, -5 and -4.


hope ot help you.....