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

The numbers are suppose to be natural numbers that is positive integers form 1 upward. So the numbers will be 5 and 6.

Step-by-step explanation:

The product of 2 consecutive natural numbers is 19 greater than their sum. We need to understand important terms in this question like consecutive and natural numbers.

Consecutive numbers are numbers that follows each other continuously from smallest to largest. Natural numbers are numbers that includes all the positive numbers from 1 to infinity example 1, 2, 3, 4 ... infinity.

Let the consecutive number be a and a+1.

The product of this 2 numbers are when you multiply them. Therefore,

a (a + 1) = a² + a

The sum of the 2 numbers are their addition. Therefore,

a + (a + 1) = 2a + 1

The product is 19 greater than the sum. This means the product of this numbers minus the sum of this numbers is equals to 19.

a² + a - (2a + 1) = 19

a² + a - 2a - 1 = 19

a² - a - 20 = 0

Find the numbers that can be multiplied to get - 20 and added together to get - 1. The numbers are 4 and - 5

a² + 4a - 5a - 20 = 0

a (a + 4) - 5 (a + 4) = 0

(a + 4) (a - 5) = 0

a = - 4 and a = 5

The numbers are suppose to be natural numbers that is positive integers from 1 upward. So the numbers will be 5 and 6.

To prove it

5 * 6 = 30 (products)

5 + 6 = 11 (sum)

30 - 11 = 19