SOLUTION: What is the smallest of 3 consecutive positive integers,if the product of the 2 smaller integers is 5 less than 5 times the largest integer?

Question 955168: What is the smallest of 3 consecutive positive integers,if the product of the 2 smaller integers is 5 less than 5 times the largest integer?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Smallest integer=n; middle integer=n+1; largest integer=n+2
(n)(n+1)=5(n+2)-5

Subtract (5n+5) from each side.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=36 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, -1. Here's your graph:

n=5 ANSWER: The smallest integer is 5.
CHECK:
middle integer=n+1=5+1=6
largest integer=n+2=5+2=7
Product of two smaller is 5 less than 5 times larger:
5(6)=5(7)-5
30=35-5
30=30
RELATED QUESTIONS
what is the smallest of 3 consecutive positive integers if the product of the smaller two (answered by CubeyThePenguin)

What is the smallest of 3 consecutive positive integers if the product of the smaller two (answered by CubeyThePenguin)

what is the smallest of 3 consecutive positive integers if the product of the smaller... (answered by Edwin McCravy)

I was needing a little help on this problem: What is the smallest of 3 consecutive... (answered by rothauserc)

The product of two consecutive positive integers is 12 more than 5 times the smaller... (answered by macston)

What is the largest of 4 consecutive positive integers if product of the middle two... (answered by stanbon)

The product of two positive consecutive odd integers is 1 less than 5 times their sum.... (answered by KMST)

what is the 3 consecutive positive integers if the product two integers is 5 less than 5... (answered by MathLover1)