Mathematics: 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

5.25 dollars for the protein shake and 4.5 for the strawberry smoothies...

Solve for z. square root(z^2 + 5 - 2 = z) what

eranique1145

12.03.2022

We have

$\sqrt{z^2-5}-2 = z$

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

$\sqrt{z^2-5}= z+2$

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.

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