Respuesta :
Answer:
{1,-1}
Step-by-step explanation:
Let's do both!
Factoring!
x^2-1 is a difference of squares.
The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So we want to solve the equation x^2-1=0 which is equivalent to solving
(x-1)(x+1)=0.
If you have A*B=0 then either A=0 or B=0.
So in our case we have x-1=0 or x+1=0.
Now we just solve the equations.
x-1=0 can be solved by adding 1 on both sides giving us x=1.
x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.
Square root!
When you want to use square roots, you have to have a perfect square containing the variables and a constant. We have that here.
We have x^2-1=0 which is equivalent to x^2=1. You could get this last equation by adding one on both sides of x^2-1=0.
Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]\sqrt{x^2}=\sqrt{1}[/tex]
[tex]x=\pm \sqrt{1}[/tex] It leads to two answers because [tex]\sqrt{x^2}=|x|[/tex].
[tex]x=\pm 1[/tex]
