Answer:
[tex]x=\pm 3\text{ or } x=\pm 2i[/tex]
Step-by-step explanation:
So we have the equation:
[tex]x^4-5x^2-36=0[/tex]
Let's let u equal x² so:
[tex]u^2-5u-36=0[/tex]
Factor. We can use -9 and 4. So:
[tex]u^2+4u-9u-36=0[/tex]
From the first two terms, factor out a u.
From the last two terms, factor out a -9. So:
[tex]u(u+4)-9(u+4)=0[/tex]
Grouping:
[tex](u-9)(u+4)=0[/tex]
Zero Product Property:
[tex]u-9=0 \text{ or } u+4=0[/tex]
On the left, add 9. On the right, subtract 4:
[tex]u=9\text{ or } u=-4[/tex]
Substitute back u:
[tex]x^2=9\text{ or } x^2=-4[/tex]
Take the square root:
[tex]x=\pm 3\text{ or } x=\pm 2i[/tex]
And we're done!
Our answer is the Second option.
