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# help algebra

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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.

Hello Guest!

$$Replace\ z^2\ with\ x.$$

$$x^2-4x+4=0$$

p          q

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

$$Replace\ x\ with\ z ^ 2.$$

$$z^2=2\\ z=\pm \sqrt{2}$$

$$z\in \{-\sqrt{2},\sqrt{2}\}$$

$$z\in \{-1.414,1.414\}$$

!

Aug 27, 2021