The product of two consecutive integers is −8 more than the square of the smaller one. Find the integers.

Answer 1

Two consecutive integers means one number right after another, like 4 & 5 or 77 & 78 or -1 & 0. But we don't know where the numbers start, so let's say "x" (the smaller number), then the next number would be "x+1."

[Note: they must be integers, so that means that it cannot be a decimal.]

Translate "The product of two consecutive integers is -8 more than the square of the smaller one."

x(x + 1) = x² - 8 Distribute the x on the left side.

x² + x = x² - 8 Combine like terms and solve for x. (The x² will cancel.)

x = - 8 x is the smaller number. Now substitute x into x + 1 to find the next number.

x + 1 = -8 + 1 = -7 So x = -8 and x + 1 = -7. -8 & -7 are indeed consecutive integers.

Check both sides:

x(x + 1) = x² - 8

-8(-8 + 1) = (-8)² - 8

56 = 56

Answer 2

The product of two consecutive integers is −8 more than the square of the smaller one. Find the integers.

Hello Mark,

Let the integers be a and b

a<b

a.b = a² - 8

also b= a+1 ( consecutive integers)

a. (a+1) = a² -8 Plugged in b

a²+a = a² - 8

gives a= - 8

b= a+1 = - 7