Question

resolva a equação biquadrada x⁴+x²+16=0​

Answer 1

A equação é falsa para qualquer valor de x.

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{x^4 + x^2 + 16 = 0}$

$\mathsf{y = x^2}$

$\mathsf{y^2 + y + 16 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = 1^2 - 4.1.16}$

$\mathsf{\Delta = 1 - 64}$

$\boxed{\boxed{\mathsf{\Delta = -63}}}\rightarrow\textsf{n{\~a}o possui ra{\'i}zes em }\mathbb{R}$

$\mathsf{y = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-1 \pm \sqrt{-63}}{2} \rightarrow \begin{cases}\mathsf{y' = \dfrac{-1 + \sqrt{63}\:i}{2}}\\\\\mathsf{y'' = \dfrac{-1 - \sqrt{63}\:i}{2}}\end{cases}}$

$\mathsf{x^2 = \dfrac{-1 + \sqrt{63}\:i}{2}}$

$\mathsf{x' = \pm\: \sqrt{\dfrac{-1 + \sqrt{63}\:i}{2}}}$

$\mathsf{x^2 = \dfrac{-1 - \sqrt{63}\:i}{2}}$

$\mathsf{x'' = \pm\: \sqrt{\dfrac{-1 - \sqrt{63}\:i}{2}}}$

$\boxed{\boxed{\mathsf{S = \{\sqrt{\dfrac{-1 + \sqrt{63}\:i}{2}};-\sqrt{\dfrac{-1 + \sqrt{63}\:i}{2}}; \sqrt{\dfrac{-1 - \sqrt{63}\:i}{2}};-\sqrt{\dfrac{-1 - \sqrt{63}\:i}{2}}\}}}}$