SOLUTION: what is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 11 more than 5 times the largest integer

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: what is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 11 more than 5 times the largest integer       Log On


   

Question 971109: what is the smallest of 3 consecutive positive integers if the product of the
smaller two integers is 11 more than 5 times the largest integer
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
what is the smallest of 3 consecutive positive integers if the product of the
smaller two integers is 11 more than 5 times the largest integer 
n%28n%2B1%29%22%22=%22%225%28n%2B2%29%2B11

n%5E2%2Bn%22%22=%22%225n%2B10%2B11

n%5E2%2Bn%22%22=%22%225n%2B21

Get 0 on the right side:

n%5E2-4n-21%22%22=%22%22%220%22

Factor the left side:

%28n-7%29%28n%2B3%29%22%22=%22%22%220%22

Set each factor = 0

n-7 = 0;  n+3 = 0
  n = 7;    n = -3

Since the problem specifically states "positive": 
we ignore the negative answer.

Answer: 7,8,9

Checking product of smaller two = 7*8 = 56

5 times the largest = 5*9 = 45

11 more than 45 is 56.

So the solution 7,8,9 is correct.
  
Edwin