Question

Qual alternativa que não representa a raiz da equação x4 - 5x2 + 4= 0​

Answer 1

Explicação passo-a-passo:

$\sf x^4-5x^2+4=0$

$\sf x^2=y$

$\sf (x^2)^2-5x^2+4=0$

$\sf y^2-5y+4=0$

$\sf \Delta=b^2-4\cdot a\cdot c$

$\sf \Delta=(-5)^2-4\cdot1\cdot4$

$\sf \Delta=25-16$

$\sf \Delta=9$

$\sf y=\dfrac{-b\pm\sqrt{\Delta}}{2\cdot a}$

$\sf y=\dfrac{-(-5)\pm\sqrt{9}}{2\cdot1}=\dfrac{5\pm3}{2}$

$\sf y'=\dfrac{5+3}{2}~\longrightarrow~y'=\dfrac{8}{2}~\longrightarrow~y'=4$

$\sf y"=\dfrac{5-3}{2}~\longrightarrow~y"=\dfrac{2}{2}~\longrightarrow~y"=1$

• Para $\sf y'=4$:

$\sf x^2=4$

$\sf x=\pm\sqrt{4}$

$\sf x=\pm2$

• Para $\sf y"=1$:

$\sf x^2=1$

$\sf x=\pm\sqrt{1}$

$\sf x=\pm2$

$\sf S=\{-2,-1,1,2\}$