Question

Which of the following is a solution to the equation 4x^5+4x^3=360x? (Note: i = root -1)

A) -10
B) -i root 10
C) 10i
D) root 10

Answer 1

`-i√(10)` (-i root 10)

Explanation:

1. Rewrite the equation:

`4x^5+4x^3=360x` | divide by
`x`,
`x` is assumed not being zero

`4x^4+4x^2=360` | rearrange and divide by
`4`

`x^2(x^2+1)=90`

2. Substitute
`-i√(10)`, to the equation:

`(-i√(10))^2((-i√(10))^2+1)=90`

calculate that
`(-i√(10))^2=-10`, and substitute to find

`-10*(-10+1)=90`

`90=90`, and the equation holds.

3. We can substitute
`10i`,
`10` and
`√(10)`, too, and find:

`(10i)^2((10i)^2+1)=-100*(-100+1)=9900` doesn't equal
`90`,

`10^2(10^2+1)=100*(100+1)=10100`, doesn't equal
`90`

`√(10)^2(√(10)^2+1)=10*(10+1)=110` that isn't equal to
`90`