Question

If the product of two consecutive odd integers is decreased by 3, the result is 12. How do you find the integers?

Answer 1

the integers are `3` and `5`
Also the integers are `-3` and `-5`

Explanation:

The solution

Let `2n+1` be the odd integer
Let `2n+3` be the next odd integer

`(2n+1)(2n+3)-3=12`

`4n^2+8n+3-3=12`

`4n^2+8n=12`

`n^2+2n=3`

`n^2+2n-3=0`

Solution by factoring

`(n-1)(n+3)=0`

`n-1=0`
`n=1`

Let `2n+1` be the odd integer which is equal `=3`
Let `2n+3` be the next odd integer which is equal `=5`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

At `n+3=0`

`n=-3`
Let `2n+1` be the odd integer which is equal `=-5`
Let `2n+3` be the next odd integer which is equal `=-3`

Checking: using odd numbers 3, and 5
`(2n+1)(2n+3)-3=12`
`(3)(5)-3=12`
`12=12" "`correct

Checking: using odd numbers -5, and -3
`(2n+1)(2n+3)-3=12`
`(-5)(-3)-3=12`
`12=12" "`correct

God bless....I hope the explanation is useful.