Answer:
[tex]a = \{1,4,9,16,25,36,49,64,81,100\}[/tex]
Step-by-step explanation:
Given
[tex]ax^2 - 64[/tex]
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 [tex]a = k^2[/tex] where [tex]k \ge 1[/tex]
When k = 1
[tex]a = 1^2 = 1[/tex]
k = 2
[tex]a = 2^2 = 4[/tex]
k=3
[tex]a = 3^2 = 9[/tex]
It goes on until k = 10
[tex]a = 10^2 = 100[/tex]
So, the possible values of a are:
[tex]a = \{1,4,9,16,25,36,49,64,81,100\}[/tex]
