Question

A] B] C] D] E] [da uma ajuda]

Answer 1

Resposta:

C

Explicação passo-a-passo:

$x^4-10x^2+9=0$

Seja $y=x^2$

$y^2-10y+9=0$

$\Delta=(-10)^2-4\cdot1\cdot9$

$\Delta=100-36$

$\Delta=64$

$y=\dfrac{-(-10)\pm\sqrt{64}}{2\cdot1}=\dfrac{10\pm8}{2}$

$y'=\dfrac{10+8}{2}~\longrightarrow~y'=\dfrac{18}{2}~\longrightarrow~y'=9$

$y"=\dfrac{10-8}{2}~\longrightarrow~y"=\dfrac{2}{2}~\longrightarrow~y"=1$

Para $y=9$, temos:

$x^2=9$

$x=\pm\sqrt{9}$

$x_1=3$

$x_2=-3$

Para $y=1$, temos:

$x^2=9$

$x=\pm\sqrt{1}$

$x_3=1$

$x_4=-1$

Logo:

$\sqrt{x_1^2+x_2^2+x_3^2+x_4^2}=\sqrt{3^2+(-3)^2+1^2+(-1)^2}$

$\sqrt{x_1^2+x_2^2+x_3^2+x_4^2}=\sqrt{9+9+1+1}$

$\sqrt{x_1^2+x_2^2+x_3^2+x_4^2}=\sqrt{20}$

Letra C