Question

19. A quadratic equation is shown below.

a2-b=0

If b is a perfect square, which represents the solutions to the equation?

HELP PLEASE

Answer 1

`\{\sqrt b, -\sqrt b\}`

Explanation:

Given

`a^2 - b = 0`

Required

Determine the solution

Since b is a perfect square, the equation can be expressed as:

`a^2 - (\sqrt b)^2 = 0`

Apply difference of two squares:

`(a - \sqrt b)(a + \sqrt b) = 0`

Split:

`(a - \sqrt b)= 0 \ or\ (a + \sqrt b) = 0`

Remove brackets:

`a - \sqrt b= 0 \ or\ a + \sqrt b = 0`

Make a the subject in both equations

`a =\sqrt b \ or\ a =-\sqrt b`

The solution can be represented as:

`\{\sqrt b, -\sqrt b\}`