Question

The sum of two consecutive positive integers and their product is `271`. What are the integers?

Answer 1

`135,136`

Explanation:

`"let "x " be one of the integers "x>0`

then the next integer is`" " x+1`

we have the sum equalling `271`

`x+x=1=271`

`2x=1=270`

`=>2x=270`

=>x=270/2=135#

`:." the integers are: "135,136`

Answer 2

The two integers are `15` and `16`.

Explanation:

Suppose the lesser of the two integers is `n`.

Then we are given:

`n + (n+1) + n(n+1) = 271`

Multiplying out and simplifying the left hand side, this becomes:

`n^2+3n+1 = 271`

Subtracting `271` from both sides, this becomes:

`0 = n^2+3n-270 = (n+18)(n-15)`

So `n=-18` or `n=15`.

Discard `n=-18` since we are looking for positive integers.

So `n=15` and the two integers are: `15` and `16`.