Answer:
-4 and 4
Step-by-step explanation:
Method 1
Apply Difference of Two Squares Formula: [tex]a^2-b^2=(a+b)(a-b)[/tex]
Given [tex]x^2-16=0[/tex]
Rewrite 16 as 4²
Therefore, [tex]a^2=x^2[/tex] and [tex]b^2=4^2[/tex]
[tex]\implies a = \sqrt{x^2}=x[/tex]
[tex]\implies b=\sqrt{4^2} =4[/tex]
[tex]\implies x^2-16^2=(x+4)(x-4)[/tex]
[tex]\implies (x+4)(x-4)=0[/tex]
[tex]\implies (x+4)=0 \implies x=-4[/tex]
[tex]\implies (x-4)=0 \implies x=4[/tex]
Method 2
Given equation:
[tex]x^2-16=0[/tex]
Add 16 to both sides:
[tex]\implies x^2-16+16=0 + 16[/tex]
[tex]\implies x^2=16[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{16}[/tex]
[tex]\implies x=\pm4[/tex]
Therefore, x = -4, x = 4
