Question

Ms ajudem pfv
observe as equações biquadradas e calcule suas raízes, onde x2=y:x4-20x2+36=0

Answer 1

$\mathsf{x^4-20x^2+36=0}\\\\\mathsf{Fixemos~~x^2=y}\\\\\mathsf{y^2-20y+36=0}\\\\\textsf{Para resolver a equa\c{c}\~ao quadr\'atica irei completar o quadrado}\\\\\mathsf{y^2-20y=-36}\\\\\mathsf{y^2-20y+100=64}\\\\\mathsf{(y-10)^2=64}\\\\\mathsf{\sqrt{(y-10)^2}=\sqrt{64}}\\\\\mathsf{|y-10|=8}\\\\\mathsf{y-10=\pm~8}$


$\begin{Bmatrix}\mathsf{y-10=+8~\rightarrow~y=18}\\\\\mathsf{ou}\\\\\mathsf{y-10=-8~\rightarrow~y=2}}\end.\\\\\\\\\mathsf{Mas~x^2=y~ent\~ao:}\\\\\\\begin{Bmatrix}\mathsf{x^2=18~\rightarrow~\sqrt{x^2}=\sqrt{18}~\rightarrow~|x|=\sqrt{18}~\rightarrow~x=\pm\sqrt{18}~\rightarrow~x=\pm3\sqrt{2}}\\\\\mathsf{ou}\\\\\mathsf{x^2=2~\rightarrow~\sqrt{x^2}=\sqrt{2}~\rightarrow~|x|=\sqrt{2}~\rightarrow~x=\pm\sqrt{2}}\end.$


$\fbox{ \mathsf{S=\begin{Bmatrix}\mathsf{-3\sqrt{2},-\sqrt{2},~\sqrt{2},~3\sqrt{2}}\end{Bmatrix}} }$