Answer:
[tex]\{\sqrt b, -\sqrt b\}[/tex]
Step-by-step explanation:
Given
[tex]a^2 - b = 0[/tex]
Required
Determine the solution
Since b is a perfect square, the equation can be expressed as:
[tex]a^2 - (\sqrt b)^2 = 0[/tex]
Apply difference of two squares:
[tex](a - \sqrt b)(a + \sqrt b) = 0[/tex]
Split:
[tex](a - \sqrt b)= 0 \ or\ (a + \sqrt b) = 0[/tex]
Remove brackets:
[tex]a - \sqrt b= 0 \ or\ a + \sqrt b = 0[/tex]
Make a the subject in both equations
[tex]a =\sqrt b \ or\ a =-\sqrt b[/tex]
The solution can be represented as:
[tex]\{\sqrt b, -\sqrt b\}[/tex]
