The product of two consecutive positive integers is 5 more than their sum. Find the integers.

Solution:

Let the two consecutive positive integers be x and (x + 1).

We have to find the integers.

Product of integers = 5 + sum of the integers.

x(x + 1) = 5 + x + x + 1

x² + x = 5 + 2x + 1

x² + x - 2x = 6

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

So, x + 2 = 0

x = -2

x - 3 = 0

x = 3

Given, the integers are positive.

So, x = 3

x + 1 = 3 + 1 = 4

Therefore, the integers are 3 and 4.

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The product of two consecutive positive integers is 5 more than their sum. Find the integers.

Summary:

The product of two consecutive positive integers is 5 more than their sum. The integers are 3 and 4.