Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{x^4 + x^2 + 16 = 0}[/tex]
[tex]\mathsf{y = x^2}[/tex]
[tex]\mathsf{y^2 + y + 16 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = 1^2 - 4.1.16}[/tex]
[tex]\mathsf{\Delta = 1 - 64}[/tex]
[tex]\boxed{\boxed{\mathsf{\Delta = -63}}}\rightarrow\textsf{n{\~a}o possui ra{\'i}zes em }\mathbb{R}[/tex]
[tex]\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-1 \pm \sqrt{-63}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{-1 + \sqrt{63}\:i}{2}}\\\\\mathsf{y'' = \dfrac{-1 - \sqrt{63}\:i}{2}}\end{cases}}[/tex]
[tex]\mathsf{x^2 = \dfrac{-1 + \sqrt{63}\:i}{2}}[/tex]
[tex]\mathsf{x' = \pm\: \sqrt{\dfrac{-1 + \sqrt{63}\:i}{2}}}[/tex]
[tex]\mathsf{x^2 = \dfrac{-1 - \sqrt{63}\:i}{2}}[/tex]
[tex]\mathsf{x'' = \pm\: \sqrt{\dfrac{-1 - \sqrt{63}\:i}{2}}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{\sqrt{\dfrac{-1 + \sqrt{63}\:i}{2}};-\sqrt{\dfrac{-1 + \sqrt{63}\:i}{2}}; \sqrt{\dfrac{-1 - \sqrt{63}\:i}{2}};-\sqrt{\dfrac{-1 - \sqrt{63}\:i}{2}}\}}}}[/tex]
