Question

Solve for z. square root(z^2 + 5 - 2 = z) What is the root? If there is no root, choose none. z = 1/4 z = 1/2 z = 4/9 none

Answer 1

z=1/4 on odyssey

Explanation:

Answer 2

We have

`√(z^2-5)-2 = z`

Isolate the square root (I'll explain why in a minute):

`√(z^2-5)= z+2`

A square root is always positive. So, if
`z+2` equals the square root of something, it must be positive. So, we must impose

`z+2\geq 0 \iff z \geq -2`

So, we will only accept solutions which are greater than or equal to -2. With that said, let's square both sides:

`z^2-5= z^2+4z+4`

We can simplify z^2, since it appears in both sides:

`-5= 4z+4`

subtract 4 from both sides:

`-9= 4z`

Finally, divide both sides by 4:

`z = \cfrac{-9}{4} = -2.25`

This number is not greater than -2, so we can't accept the solution.