Question

qunatas soluções reias tem a equação (x²+1)² +6 × (x²+1) +8=0​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{(x^2 + 1)^2 + 6\:.\:(x^2 + 1) + 8 = 0}$

$\mathsf{y = x^2 + 1}$

$\sf{y^2 + 6y + 8 = 0}$

$\sf{y^2 + 6y + 8 + 1 = 0 + 1}$

$\sf{y^2 + 6y + 9 = 1}$

$\sf{(y + 3)^2 = 1}$

$\sf{y + 3 = \pm\: 1}$

$\mathsf{y' = 1 - 3 = -2}$

$\mathsf{y'' = -1 - 3 = -4}$

$\mathsf{x^2 + 1 = -2}$

$\mathsf{x^2 = -3}$

$\mathsf{x = \pm\:\sqrt{3}\:i}$

$\mathsf{x^2 + 1 = -4}$

$\mathsf{x^2 = -5}$

$\mathsf{x = \pm\:\sqrt{5}\:i}$

$\boxed{\boxed{\sf{S = \{\sqrt{3}\:i;\:-\sqrt{3}\:i;\:\sqrt{5}\:i;\:-\sqrt{5}\:i\}}}}\leftarrow\textsf{zero ra{\'i}zes reais}$