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=-√(10) \ \lor \ x=√(10) \ \lor \ x=-√(-10) \ \lor \ x=√(-10) \\ \boxed{x=-√(10) \hbox{ or } x=√(10) \hbox{ or } x=-i√(10) \hbox{ or } x=i√(10)}`