Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\sf{(x^2 + 1)^2 + 6\:.\:(x^2 + 1) + 8 = 0}[/tex]
[tex]\mathsf{y = x^2 + 1}[/tex]
[tex]\sf{y^2 + 6y + 8 = 0}[/tex]
[tex]\sf{y^2 + 6y + 8 + 1 = 0 + 1}[/tex]
[tex]\sf{y^2 + 6y + 9 = 1}[/tex]
[tex]\sf{(y + 3)^2 = 1}[/tex]
[tex]\sf{y + 3 = \pm\: 1}[/tex]
[tex]\mathsf{y' = 1 - 3 = -2}[/tex]
[tex]\mathsf{y'' = -1 - 3 = -4}[/tex]
[tex]\mathsf{x^2 + 1 = -2}[/tex]
[tex]\mathsf{x^2 = -3}[/tex]
[tex]\mathsf{x = \pm\:\sqrt{3}\:i}[/tex]
[tex]\mathsf{x^2 + 1 = -4}[/tex]
[tex]\mathsf{x^2 = -5}[/tex]
[tex]\mathsf{x = \pm\:\sqrt{5}\:i}[/tex]
[tex]\boxed{\boxed{\sf{S = \{\sqrt{3}\:i;\:-\sqrt{3}\:i;\:\sqrt{5}\:i;\:-\sqrt{5}\:i\}}}}\leftarrow\textsf{zero ra{\'i}zes reais}[/tex]
