Answer:
8 and 9
Step-by-step 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]
