Solve for integers

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?

Answer 1

Three consecutive integers: n, n+1, n+2

n(n+1) = 5(n+2) - 5

 

Can you solve for n and answer?

Answer 2

The 3 integers are

 

n  [the smallest]

n + 1

n + 2

 

n(n + 1) = 5(n + 2) - 5

n² + n = 5n + 5

n² - 4n - 5 = 0

(n + 1)(n - 5) = 0

 

The positive solution is

 

n = 5