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

 Aug 26, 2021
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Find all values of z such that z^4 - 4z^2 +4 = 0.

 

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\(Replace\ z^2\ with\ x.\)

\(x^2-4x+4=0\)

       p          q

\(x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ x=2\pm \sqrt{2^2-4}\\ x=2\)

\(Replace\ x\ with\ z ^ 2. \)

\(z^2=2\\ z=\pm \sqrt{2}\)

\(z\in \{-\sqrt{2},\sqrt{2}\}\)

\(z\in \{-1.414,1.414\}\)

laugh  !

 Aug 27, 2021

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