Q. 74.0( 22 Votes )

The product of two consecutive positive integers is 306. Find the integers.

Answer :

Let the two consecutive positive integers be x and (x + 1)

According to given condition,


x(x + 1) = 306


x2 + x – 306 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 1 c = – 306


= 1. – 306 = – 306


And either of their sum or difference = b


= 1


Thus the two terms are 18 and – 17


Difference = 18 – 17 = 1


Product = 18. – 17 = – 306


x2 + x – 306 = 0


x2 + 18x – 17x – 306 = 0


x(x + 18) – 17(x + 18) = 0


(x + 18) (x – 17) = 0


(x + 18) = 0 or (x – 17) = 0


x = – 18 or x = 17


but x = 17 ( x is a positive integers)


x + 1 = 17 + 1 = 18


Thus the two consecutive positive integers are 17 and 18


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