SOLUTION: I was needing a little help on this problem: What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the larges

Question 742472: I was needing a little help on this problem:
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?
Thank you! :)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We are given
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?
let 3 consecutive positive integers be i, i+1, i+2
then we have,
i*(i+1) = 5*(i+2)-5

now, we multiply and simplify
i^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

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