If k = (n + 2)(n - 2), where n is an integer greater than 2, what is the value of k?

Solution:

Additional information is required to solve the equation as the integer “n” can assume any value greater than 2.

Given: k = (n + 2)(n - 2)

Using the known algebraic identity of the difference of squares, we know that (n + 2)(n - 2) = n²-2²

Thus k =  n²-2²

k =  n²-4

Take values > 2 for n

k = 3²-4= 5

k = 4²-4= 12

k = 5²-4=21

k = 6²-4=32

k = 7²-4= 45

and so on.

Thus the value of k ranges from 5 up to infinity. k = {5, 12, 21, 32, 45.....}

If k = (n + 2)(n - 2), where n is an integer greater than 2, what is the value of k?

Summary:

k = (n + 2)(n - 2), where n is an integer greater than 2. From the given information a single value of k cannot be found out. The value of k ranges from 5 up to infinity. k = {5, 12, 21, 32, 45.....}