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Find all values of z such that z^4 - 4z^2 +4 = 0.

 Apr 10, 2022
 #1
avatar+30 
+4

I am not the best at explaining, and I don't explain very much(new user and look at my username), so don't go attacking me. (I also skip like a lot of "simple" to me steps)

First, you can factor z^4 - 4z^2 + 4 = 0 into (z^2 -2)^2

I am assuming that you already know this, but i will still "explain"

You can turn z^4 - 4z^2 +4 = 0 into z^4 - 2z^2 - 2z^2 + 4

Then, you notice that you can factor that into z^2(z^2 - 2) -2(z^2 - 2)

Then, you can turn that into (z^2 -2)(z^2-2). Or, (z^2 - 2)^2.

You notice that \(\sqrt{2}\), will work, and -\(\sqrt{2}\)

Because, \((\sqrt{2})^2\)is equal to 0, (2-2)^2 = 0

And \((-\sqrt{2})^2\)is also equal to 2.

 

 

I hope this helped?

 Apr 10, 2022
 #2
avatar+117870 
+1

Hi IMB   (I am bad ... )

Welcome to the Web2.0calc forum!

Give yourself a point  laugh

 Apr 10, 2022
edited by Melody  Apr 10, 2022

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