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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

User Terrilyn
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2 Answers

7 votes

Answer:

z=1/4 on odyssey

Explanation:

User Vodet
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2 votes

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.

User Meraj Al Maksud
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8.8k points

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