the two consecutive odd integers can be written as

2x-1 and 2x+1, where x is integer

the difference of the squares of two consecutive odd integers is 24

(2x + 1)^2 - (2x - 1)^2 = 24

by solving we find

x = 3

click here to see the step by step solution of the equation

Click to see all the steps

2*3 + 1 = 7

2*3 - 1 = 5

indeed 7^2 - 5^2 = 49 - 25 = 24

the two integers are 5 and 7.