Answer:
11
Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
n(n + 1) = 8(n + 2) + 2 ust the distributive property
n² + n = 8n + 16 + 2
n² + n = 8n + 18 subtract 8n from both sides
n² - 7n = 18 subtract 18 from both sides
n² - 7n - 18 = 0
n² - 9n + 2n - 18 = 0
n(n - 9) + 2(n - 9) = 0
(n - 9)(n + 2) = 0 ⇔ n - 9 = 0 or n + 2 =0
n - 9 = 0 add 9 to both sides
n = 9
n + 2 = 0 subtract 2 from both sides
n = -2 < 0
n + 2 = 9 + 2 = 11
