Question

The difference of the square of two consecutive odd integers is 24. Find the integers. Show work please.

Answer 1

consecutie odd integers are 2 apart

odd integers are represented by 2n+1 where n is a whole number

so the numbers are
2n+1 and 2n+1+2

(2n+3)²-(2n+1)²=24
4n²+12n+9-(4n²+4n+1)=24
4n²+12n+9-4n²-4n-1=24
8n+8=24
minus 8 both sides
8n=16
divide by 8
n=2

2n+1 is first one
2(2)+1=4+1=5
5+2=7

the numbers are 5 and 7