Question

Find three consecutive odd integers such that the product of the first two is equal to one more than twice the third

Answer 1

`-3, -1, 1` or
`3, 5, 7`

Explanation:

Let first consecutive odd integer =
`x`

Second consecutive odd integer =
`x+2`

Third consecutive odd integer =
`x+4`

"Product of the first two is equal to one more than twice the third" can be written as:

`x(x+2)=1+2(x+4)`

`x^2+2x=1+2x+8` (expand brackets)

`x^2+2x=9+2x` (combine like terms)

`x^2=9`

`x=\pm3`

∴ Consecutive integers =
`-3, -1, 1` or
`3, 5, 7`

Hope this helps :)