Chapter 1 - Equations and Inequalities - 1.5 Applications and Modeling with Quadratic Equations - 1.5 Exercises - Page 129: 18

$$7,9$$

The difference of the squares of two consecutive odd integers equals 32, which can be represented as $(x+2)^2-(x)^2=32$ $x^2+4x+4-x^2=32$ $4x+4=32$ $4x=28$ $x=7$ Substitute $7$ for $x$ into the original equation and check $(7+2)^2-7^2=32$ $9^2-7^2=32$ $81-49=32$ $7,9$