What are the solutions to z^{4}-2z^{2}+4=0?

zgribestika

zgribestika

Answered question

2022-01-16

What are the solutions to z42z2+4=0?

Answer & Explanation

autormtak0w

autormtak0w

Beginner2022-01-17Added 31 answers

First, we split the equation into two factors, as follows:
(z2az+2)(z2+az+2)
where a is a parameter to be determined
This expands to z4+(4a2)z2+4
Therefore choosing
a=6
allows us to split the quartic into two quadratics:
(z26z+2)(z2+6z+2)=0
Then each of these factors can be solved by the quadratic formula.
The four values of z turn out to be
z=±2±62

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