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

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Answer 1 · 2017-03-18T09:21:04

$135,136$

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

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 · 2017-03-18T10:18:57

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

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 $16$ .

The sum of two consecutive positive integers and their product is 271271. What are the integers?