Question

X^4-100=0 solve the equation by factoring

Answer 1

$x^4-100=0 \\ (x^2)^2-10^2=0 \\ (x^2-10)(x^2+10)=0 \\ x^2-10=0 \ \lor \ x^2+10=0 \\ x^2=10 \ \lor \ x^2=-10 \\ x=-\sqrt{10} \ \lor \ x=\sqrt{10} \ \lor \ x=-\sqrt{-10} \ \lor \ x=\sqrt{-10} \\ \boxed{x=-\sqrt{10} \hbox{ or } x=\sqrt{10} \hbox{ or } x=-i\sqrt{10} \hbox{ or } x=i\sqrt{10}}$