Question

The product of two consecutive natural numbers is 19 greater than their sum. Find thee numbers.

Answer 1

the numbers are 9 and 10.

Explanation:

Two consecutive natural numbers can be written as

n and n +1-

Here we have that:

n*(n + 1) - (n + n + 1) = 19

now we need to solve this for n.

n^2 + n - n - n - 1 = 19

n^2 - n - 1 - 19 = 0

n^2 - n - 20 = 0

so now we have a quadratic equation, the solutions are:

`n = (1 + -√(1^2 -4*1*-20) )/(2*1) = (1 +- 9)/(2)`

So the two solutions are:

n = (1 + 9)/2 = 5

n = (1 - 9)/2 = -4

But we know that n is a natural number, so it only can be a positive integer, then the correct option is n = 9.

and the consecutive number is 9 + 1 = 10