Question

x^6+5x^3-24=0 hallar la solucion ala siguiente ecuacion

Answer 1

        $x^6+5x^3-24=0\\ \\ (x^3+8)(x^3-3)=0\\ \\ \left[(x+2)(x^2-2x+4)\right]\left[\left(x-\sqrt[3]3\right)\left(x^2+\sqrt[3]3x+\sqrt[3]3^2\right)\right]=0\\ \\ x+2=0 ~\vee~ x^2-2x+4=0~\vee~ x-\sqrt[3]3=0~\vee~x^2+\sqrt[3]3x+\sqrt[3]3^2=0\\ \\ x=-2~\vee~x=\dfrac{2\pm\sqrt{-12}}{2}~\vee~x=\sqrt[3]3~\vee~x=\dfrac{-\sqrt[3]3\pm\sqrt{-3\sqrt[3]3}}{2}\\ \\ \\ x\in\left\{-2,1-\sqrt{3}i,1+\sqrt{3}i,\sqrt[3]3,\dfrac{-\sqrt[3]3+\sqrt{3\sqrt[3]3}i}{2},\dfrac{-\sqrt[3]3-\sqrt{3\sqrt[3]3}i}{2}\right\}$