Question

Resolva, em R, a equações:
c)x elevado a 4+x²=2
d)x elevado a 4=x²+2

Answer 1

a)

$x^4+x^2=2\\ \\ x^4+x^2-2=0\\ \\ \boxed{y=x^2}\\ \\ y^2+y-2=0\\ \\ \Delta=1^2-4.1.(-2)=1+8=9\\ \\ y=\frac{-1\pm\sqrt9}{2}=\frac{-1 \pm 3}{2}\\ \\ y_1=-2\\ \\ y_2=1\\ \\ x^2=1\rightarrow x=\pm1\\ \\ S=\{\pm 1\}$

b)
$x^4=x^2+2\\ \\ x^4-x^2-2=0\\ \\ \boxed{y=x^2}\\ \\ y^2-y-2=0\\ \\ \Delta=(-1)^2-4.1.(-2)=9\\ \\ y=\frac{1\pm3}{2}\\ \\ y_1=1\\ \\ y_2=2\\ \\ x^2=1 \rightarrow x= \pm1\\ \\ x^2=2 \rightarrow x= \pm \sqrt{2} \\ \\ S=\{ \pm1;\pm \sqrt{2}\}$