Question

For what natural values of n is the value of each expression to a natural number?:
(5n-12)/n
and
(36-n^2)/n^2

Answer 1

Answer:

n = 3, 4, 6, 12 and n = 1, 2, 3

Step-by-step explanation:

(5n-12)/n = 5-12/n

For 12/n to be natural, n = 1, 2, 3, 4, 6, 12

But, 5-12/n must be >= 1. Therefore, n = 3, 4, 6, 12

(36-n^2)/n^2 = 36/n^2 - 1

For 36/n^2 to be natural, n^2 = 1, 2, 3, 4, 6, 9, 18, 36

Then, n = +- 1, += sqrt(2), +-sqrt(3), +-2, +-sqrt(6), +-3, +-sqrt(18), +-6

But, n must be natural. Then, n = 1, 2, 3, 6

But, 36/n^2 - 1 >= 1. Therefore, n = 1, 2, 3