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

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