Question

The polynomial ax2 − 64 is a difference of two squares. Find all possible values of a between 1 and 100 inclusive. The inclusive values are

Answer 1

`a = \{1,4,9,16,25,36,49,64,81,100\}`

Explanation:

Given

`ax^2 - 64`

Required

Determine possible values of a

For the expression to be a difference of two squares, then a must be a perfect square between 1 and 100 (inclusive).

Let
`a = k^2` where
`k \ge 1`

When k = 1

`a = 1^2 = 1`

k = 2

`a = 2^2 = 4`

k=3

`a = 3^2 = 9`

It goes on until k = 10

`a = 10^2 = 100`

So, the possible values of a are:

`a = \{1,4,9,16,25,36,49,64,81,100\}`