Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
[tex]x^4+x^2-6=0 \\
(x^2)^2+x^2-6=0 \\ \\
a=1 \\ b=1 \\ c=-6 \\ b^2-4ac=1^2-4 \times 1 \times (-6)=1+24=25 \\ \\
x^2=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-1 \pm \sqrt{25}}{2 \times 1}=\frac{-1 \pm 5}{2} \\
x^2=\frac{-1-5}{2} \ \lor \ x^2=\frac{-1+5}{2} \\
x^2=\frac{-6}{2} \ \lor \ x^2=\frac{4}{2} \\
x^2=-3 \ \lor \ x^2=2 \\
x=\pm \sqrt{-3} \ \lor \ x=\pm \sqrt{2} \\
\boxed{x=-i\sqrt{3} \hbox{ or } x=i\sqrt{3} \hbox{ or } x=-\sqrt{2} \hbox{ or } x=\sqrt{2}}[/tex]
[tex]x^4+x^2-6=0\\
x^4+3x^2-2x^2-6=0\\
x^2(x^2+3)-2(x^2+3)=0\\
(x^2-2)(x^2+3)=0\\
x^2-2=0 \vee x^2+3=0\\
x^2=2 \vee x^2=-3\\
x=-\sqrt2 \vee x=\sqrt2 \vee x=-i\sqrt3 \vee x=i\sqrt3[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.