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

Define x:

Let one of the number be x.

One number = x

The other consecutive number = x + 1

Form equation:

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

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

Solve x:

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

Distribute x:

x² + x = x + x + 1 + 5

Combine like terms:

x² + x = 2x + 6

Subtract 2x + 6 from both sides:

x² - x - 6 = 0

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

x = 3 or x = -2

Find the two integers:

If x = 3:

One number = x = 3

The other consecutive number = x + 1 = 3 + 1 = 4

If x = -2:

One number = x = -2

The other consecutive number = x + 1 = -2 + 1 = -1

The two possible answer is 3 and 4 or -2 and -1

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