Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{x^4 + 3x^2 - 4 = 0}[/tex]
[tex]\mathsf{y = x^2}[/tex]
[tex]\mathsf{y^2 + 3y - 4 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (3)^2 - 4.1.(-4)}[/tex]
[tex]\mathsf{\Delta = 9 + 16}[/tex]
[tex]\mathsf{\Delta = 25}[/tex]
[tex]\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-3 \pm \sqrt{25}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{-3 + 5}{2} = \dfrac{2}{2} = 1}\\\\\mathsf{y'' = \dfrac{-3 - 5}{2} = \dfrac{-8}{2} = -4}\end{cases}}[/tex]
[tex]\mathsf{x^2 = 1}[/tex]
[tex]\mathsf{x = \pm\:\sqrt{1}}[/tex]
[tex]\mathsf{x = \pm\:1}[/tex]
[tex]\mathsf{(-1)^2 = 1}[/tex]
[tex]\mathsf{(1)^2 = 1}[/tex]
[tex]\textsf{Acredito que essa seja sua d{\'u}vida. Ambas ra{\'i}zes atendem.}}[/tex]
[tex]\mathsf{i^2 = -1}[/tex]
[tex]\mathsf{x^2 = -4}[/tex]
[tex]\mathsf{x = \pm\:\sqrt{-4}}[/tex]
[tex]\mathsf{x = \pm\:\sqrt{4.(-1)}}[/tex]
[tex]\mathsf{x = \pm\:\sqrt{4}.\sqrt{-1}}}[/tex]
[tex]\mathsf{x = \pm\:2i}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{1;-1;2i;-2i\}}}}[/tex]
