Question

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 1

11

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