Question

the sum of two consecutive numbers is 11

Answer 1

The required number is 5 and 6.

Answer 2

If the integers are

m and m+1

, then we are given:m×(m+1)

=m+(m+1)+11

That is: m2+m=2m+12

Subtract  2m+12 from both sides to get:

0=m2−m−12=(m−4)(m+3)

This equation has solutions

m=−3 and m=4

We were told that

m and m+1

are positive, so we can reject

m=−3

, leaving the unique solution

m=4.So the integers are m=4 and m+1=5.