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

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asked Apr 13, 2019 190k views

2 Answers

Meraj Al Maksud · Answer 1 · 2019-04-20T04:33:58+0000

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.