Question

What are the solution(s) of the equation?
- 5x4 + 16x? + 32x= - 6x4 - 2x3

Answer 1

The solutions are:

x=0, x=-2, x=4i, x=-4i

Explanation:

We need to find solutions of the equation
`- 5x^4 + 16x^2 + 32x= - 6x^4 - 2x^3`

Note in given question:
`- 5x^4 + 16x? + 32x= - 6x^4 - 2x^3` considering 2 instead of ?

Solving:

`- 5x^4 + 16x^2 + 32x= - 6x^4 - 2x^3`

`- 5x^4 + 16x^2 + 32x+ 6x^4 + 2x^3=0\\- 5x^4+ 6x^4 + 16x^2 + 32x + 2x^3=0\\x^4+2x^3+16x^2+32x=0`Taking x common

`x(x^3+2x^2+16x+32)=0\\x=0 \ or \ x^3+2x^2+16x+32=0`

`Simplifying \ x^3+2x^2+16x+32=0 \ we \ get (x+2)(x^2+16)`

`x=0 \ or \ (x+2)(x^2+16)=0\\x=0 \ or \ x+2=0 \ or x^2+16=0\\x=0 \ or \ x=-2 \ or x^2=-16\\We \ know \ √(-1)=i \\x=0 \ or \ x=-2 \ or x=\pm 4i\\`

So, the solutions are:

x=0, x=-2, x=4i, x=-4i