Question

resolva a equaçao sendo U=R:

1/1+x²+10/x²+1=x²/10

Answer 1

$\frac{1}{1+x^2}+\frac{10}{x^2+1}=\frac{x^2}{10} \\ \\ \frac{11}{x^2+1}=\frac{x^2}{10} \\ \\ x^4+x^2-110=0 \\ \\ \boxed{y=x^2} \\ \\ y^2+y-110=0 \\ \Delta=1^2-4.1.(-110)=1+440=441 \\ \\ y_1=\frac{-1-21}{2}=-11 \\ \\ y_2=\frac{-1+21}{2}= 10 \\ \\ x_1=+\sqrt{10} \\ \\ x_2=-\sqrt{10} \\  \\  x_3=+\sqrt{11}i \\ \\ x_4=\sqrt{11}i$