Respuesta :
We have
[tex] \sqrt{z^2-5}-2 = z [/tex]
Isolate the square root (I'll explain why in a minute):
[tex] \sqrt{z^2-5}= z+2 [/tex]
A square root is always positive. So, if [tex] z+2 [/tex] equals the square root of something, it must be positive. So, we must impose
[tex] z+2\geq 0 \iff z \geq -2 [/tex]
So, we will only accept solutions which are greater than or equal to -2. With that said, let's square both sides:
[tex] z^2-5= z^2+4z+4 [/tex]
We can simplify z^2, since it appears in both sides:
[tex] -5= 4z+4 [/tex]
subtract 4 from both sides:
[tex] -9= 4z [/tex]
Finally, divide both sides by 4:
[tex] z = \cfrac{-9}{4} = -2.25 [/tex]
This number is not greater than -2, so we can't accept the solution.
