Question

Determine o conjunto solução
(x²+2)²=2(x²+6)

Answer 1

$(x^2+2)^2=2(x^2+6) \\ x^4+4x^2+4=2x^2+12 \\ x^4+2x^2-8=0 \\ \\ \boxed{y=x^2} \\ \\ y^2+2y-8=0 \\ \Delta=2^2-4.1.(-8) = 4+32=36 \\ \\ y_1=\frac{-2-6}{2}=-4 \\ y_2=\frac{-2+6}{2}=2 \\ \\ x_1=-\sqrt2 \\ x_12=\sqrt2 \\ x_3=-\sqrt{-4}=-2i \\ x_3=\sqrt{-4}=2i$