Question

Calcule as raízes da equação biquadra abaixo:
m^4 – 10m^2 + 9 = 0

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{m^4 - 10m^2 + 9 = 0}$

$\mathsf{x = m^2}$

$\mathsf{x^2 - 10x + 9 = 0}$

$\mathsf{x^2 - 10x + 9 + 16 = 16}$

$\mathsf{x^2 - 10x + 25 = 16}$

$\mathsf{(x - 5)^2 = 16}$

$\mathsf{x - 5 = \pm\:\sqrt{16}}$

$\mathsf{x - 5 = \pm\:4}$

$\mathsf{x'= 4 + 5 = 9}$

$\mathsf{x'' = -4 + 5 = 1}$

$\mathsf{m^2 = 9 \iff m = \pm\:\sqrt{9} \iff m = \pm\:3}$

$\mathsf{m^2 = 1 \iff m = \pm\:\sqrt{1} \iff m = \pm\:1}$

$\boxed{\boxed{\mathsf{S = \{3;-3;1;-1\}}}}$