Write equation and solve

Question

find three consecutive even integers such that the sum of the first and the third integers is one—fourth the product of the second and third integers. Give your answers as comma separated numbers in ascending order 

Answer 1

The 3 consecutive even integers are 

 

n

n + 2

n + 4

 

n + (n + 4) = (1/4)(n + 2)(n + 4)

 

2n + 4 = (1/4)(n² + 6n + 8)

8n + 16 = n² + 6n + 8

n² - 2n - 8 = 0

(n - 4)(n + 2) = 0

n = 4 or -2

 

If n = 4, the 3 consecutive even integers are 4, 6, and 8

If n = -2, the 3 consecutive even integers are -2, 0, and 2