Question

Resolva a inequação -X^4+2X^2+8 ≤ 0

Answer 1

$-x^4+2x^2+8 \leq 0$

calcular as raízes usando artifício  x²=y

$-y^2+2y+8=0 \\ \\ a=-1 \\ b=2 \\ c=8 \\ \\ \Delta=b^2-4ac \\ \Delta=2^2-4(-1)(+8) \\ \Delta=4+32 \\ \Delta=36 \\ \\ [tex]y= \frac{-b\pm \sqrt{\Delta} }{2a} = \frac{-2\pm6}{-2} \\ \\ y'= \frac{-2-6}{-2} = \frac{-8}{-2} =+4 \\ \\ y"= \frac{-2+6}{-2} = \frac{4}{-2} =-2 \\ \\ se~~x^2=y \\ \\ x^2=4 \\ x=\pm \sqrt{4} \\ x=\pm2 \\ \\ x^2=-2 \\ x=\pm \sqrt{-2} ~\not\exists~~raiz \\ \\ -----\bullet^{-2}++++++\bullete^2------ \\ \\ S=\{x\in R/x \leq -2~~ou~~x \geq 2~\}$