Mathematics: 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

The polynomial ax2 − 64 is a difference of two squares.

makayyafreeman

21.03.2021

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

Step-by-step 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:

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

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