Question

How do you find two consecutive integers whose product is 72?

Answer 1

The two consecutive integers are
either
`color(white)("XXX")-9 and -8`
or
`color(white)("XXX")8 and 9`

Explanation:

Let the smaller integer be `n`
`rarr` the larger integer will be `(n+1)`

We are told
`color(white)("XXX")nxx(n+1)=72`

`color(white)("XXX")rarr n^2+n-72=0`

`color(white)("XXX")rarr (n+9)(n-8)=0`

`color(white)("XXX")n=-9color(white)("XX")orcolor(white)("XX")n=8`