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

Mar 18, 2017

$135 , 136$

Explanation:

$\text{let "x " be one of the integers } x > 0$

then the next integer is$\text{ } x + 1$

we have the sum equalling $271$

$x + x = 1 = 271$

$2 x = 1 = 270$

$\implies 2 x = 270$

=>x=270/2=135#

$\therefore \text{ the integers are: } 135 , 136$

Mar 18, 2017

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

Explanation:

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

Then we are given:

$n + \left(n + 1\right) + n \left(n + 1\right) = 271$

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

${n}^{2} + 3 n + 1 = 271$

Subtracting $271$ from both sides, this becomes:

$0 = {n}^{2} + 3 n - 270 = \left(n + 18\right) \left(n - 15\right)$

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 $16$.