Question

Find two consecutive positive integers such that the square of the

smaller integer is nineteen more than five times the larger integer.

Answer 1

8 and 9

Explanation:

let 'n' = smaller positive integer

let 'n+1' = larger

n² = 5(n+1)+19

n² = 5n + 5 + 19

n² = 5n + 24

n² - 5n - 24 = 0

(n-8)(n+3) = 0

n = 8 [this is the smaller positive integer]

n+1 = 9 [this is the larger positive integer]

n = -3 [this value can be discounted because it is not positive]