Question

The product of two consecutive positive integer is 306. Find the interger

Answer 1

Let one integer be x then next will be x+1
their product= x(x+1)
According to question
x(x+1) =306
x^2+ x -306 =0
two number such that their sum is 1 and product is -306 are
18-17 = 1
18x-17 = -306
x^2+18x-17x-306=0
x(x+18) -17(x+18) =0
(x-17) (x+18) =0
x =17 and x=-18
since number has to be positive (according to question)
so x =17
another number is 17+1 = 18