Question

The difference of the squares of two consecutive odd integers is 72. Find both the integers. (1) Show the equation you used below (this is the one step) and (2) give the answers. [Hint: There are two sets of answers.]

Answer 1

17 and 19

Explanation:

Let

The first off number = x

Second odd number = x + 2

The difference of the squares of two consecutive odd integers is 72

(x+2)^2 - (x)^2 = 72

x^2 + 4x + 4 - x^2 = 72

4x + 4 = 72

4x + 4 - 4 = 72 - 4

4x = 68

Divide both sides by 4

x = 68/4

= 17

x = 17

The first off number = x = 17

Second odd number = x + 2

= 17 + 2

= 19