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

2 Answers
Mar 18, 2017

Answer:

#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#

Mar 18, 2017

Answer:

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#.