The difference between the squares of two positive consecutive odd integers is 24. Find the integers.

Answer 1

We just need to break it down. "Two positive consecutive odd integers" is the first clue. Consider two consecutive odd integers, 11 and 13. Let x = the first odd integer then the next is x+2. So if x=11, the next odd integer is 11+2 or 13.

The next clue is "the difference between the squares . . . is 24" so simply, (x+2)² - x² = 24

Now solve for x.

(x²+4x + 4) - x² = 24

4x+4 = 24

x+1=6

x=5

Hence, the numbers are 5 and 7.

Answer 2

Hi Isabella,

Consecutive odd integers are odd integers that come right after one another. For example, 3 and 5 are consecutive odd integers.

In this problem, we are asked to find two consecutive odd integers if the squares of those integers subtract to equal 24. We will need to set up an equation to do this.

Because we do not know the integers we can use variables x and (x-2). We use x and (x-2) because x will give you the second odd integer and (x-2) will give you the second odd integer minus 2, which equals the 1st odd integer.

We then set up the equation and solve.

x²-(x-2)²=24

x²-(x²-4x+4)=24

x²-x²+4x-4=24

4x=24+4

4x=28

x=7

x-2= (7-2) = 5

The two consecutive odd integers are 5 and 7.

Answer 3

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

x^2 + 4x + 4 - x^2 = 24

4x = 20

x = 20/4 = 5

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

the numbers are 5 and 7