24-11-2014
Mathematics

Answered

How to factor this problem with negative exponents? -4x^-4-3x^-2+1=0

Please show all steps, thanks. tsj

Verified Answer :

konrad509 konrad509

24-11-2014

\(-4x^{-4}-3x^{-2}+1=0\\ -4x^{-4}-4x^{-2}+x^{-2}+1=0\\ -4x^{-2}(x^{-2}+1)+1(x^{-2}+1)=0\\ -(4x^{-2}-1)(x^{-2}+1)=0\\ 4x^{-2}-1 =0 \vee x^{-2}+1=0\\ 4x^{-2} =1 \vee x^{-2}=-1\\ x^{-2}=\frac{1}{4} \vee \frac{1}{x^2}=-1\\ \frac{1}{x^2}=\frac{1}{4}\\ x=-2 \vee x=2\)

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