What is the largest of three consecutive positive integers if the product of the two smallest is equal to 2 more than 8 times the longest.

Answer:11Step-by-step explanation:n, n + 1, n + 2 - three consecutive integersThe equation:n(n + 1) = 8(n + 2) + 2              ust the distributive propertyn² + n = 8n + 16 + 2n² + n = 8n + 18               subtract 8n from both sidesn² - 7n = 18          subtract 18 from both sidesn² - 7n - 18 = 0n² - 9n + 2n - 18 = 0n(n - 9) + 2(n - 9) = 0(n - 9)(n + 2) = 0 ⇔ n - 9 = 0 or n + 2  =0n - 9 = 0     add 9 to both sidesn = 9n + 2 = 0          subtract 2 from both sidesn = -2 < 0n + 2 = 9 + 2 = 11