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What is the largest of three consecutive positive integers if the product of the two smallest is equ...
4 months ago
Q:
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.
Accepted Solution
A:
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