macjas wrote:
If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?
A. 12
B. 16
C. 17
D. 20
E. 48
We can simplify the given equation:
(n^3 - n)/(n + 1) = 240
n(n^2 - 1)/(n + 1) = 240
n(n + 1)(n - 1)/(n + 1) = 240
n(n - 1) = 240
n^2 - n - 240 = 0
(n - 16)(n + 15) = 0
n = 16 or n = -15
Answer: B