The product of two consecutive positive integers is 1 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 = 1 + sum of the integers.

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

x² + x = 1 + 2x + 1

x² + x = 2x + 2

x² + x - 2x - 2 = 0

x² - x - 2 = 0

x² - 2x + x - 2 = 0

x(x - 2) + 1(x - 2) = 0

(x + 1)(x - 2) = 0

So, x + 1 = 0

x = -1

x - 2 = 0

x = 2

Given, the integers are positive.

So, x = 2

x + 1 = 2 + 1 = 3

Therefore, the integers are 2 and 3.

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The product of two consecutive positive integers is 1 more than their sum. Find the integers.

Summary:

The product of two consecutive positive integers is 1 more than their sum. The integers are 2 and 3.