Answer:
[tex]-i\sqrt{10}[/tex] (-i root 10)
Step-by-step explanation:
1. Rewrite the equation:
[tex]4x^5+4x^3=360x[/tex] | divide by [tex]x[/tex], [tex]x[/tex] is assumed not being zero
[tex]4x^4+4x^2=360[/tex] | rearrange and divide by [tex]4[/tex]
[tex]x^2(x^2+1)=90[/tex]
2. Substitute [tex]-i\sqrt{10}[/tex], to the equation:
[tex](-i\sqrt{10})^2((-i\sqrt{10})^2+1)=90[/tex]
calculate that [tex](-i\sqrt{10})^2=-10[/tex], and substitute to find
[tex]-10*(-10+1)=90[/tex]
[tex]90=90[/tex], and the equation holds.
3. We can substitute [tex]10i[/tex], [tex]10[/tex] and [tex]\sqrt{10}[/tex], too, and find:
[tex](10i)^2((10i)^2+1)=-100*(-100+1)=9900[/tex] doesn't equal [tex]90[/tex],
[tex]10^2(10^2+1)=100*(100+1)=10100[/tex], doesn't equal [tex]90[/tex]
[tex]\sqrt{10}^2(\sqrt{10}^2+1)=10*(10+1)=110[/tex] that isn't equal to [tex]90[/tex]
