Answer:
the numbers are 9 and 10.
Step-by-step 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:
[tex]n = \frac{1 + -\sqrt{1^2 -4*1*-20} }{2*1} = \frac{1 +- 9}{2}[/tex]
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
