Question

What is the smallest of 3 consecutive positive integers if the product of the smaller

two integers is 5 less than 5 times the largest integer?
please explain

Answer 1

let 3 consecutive positive integers be i, i+1, i+2
then we have,
i*(i+1) = 5*(i+2)-5i^2+i = 5i+10-5
regroup and set equal to 0
i^2-4i-5=0
factor this expression into
(i-5)*(i+1) = 0
therefore i=5 or -1, we choose i=5 since our integers are to be positive
and our solution is the integers 5, 6, 7