Solve the equation X^4-8x^2-9=0?

Question

Please Show your work, thank you

Answer 1

(x^2-9)(x^2+1)=0
(x+3)(x-3)(x+i)(x-i)=0
the roots are-3,3,i,-i

Answer 2

First, let y = x^2 so
y^2 - 8y - 9 = 0, and you have a quadratic equation, whose roots can be found using the quadratic formula.
But this one is obvious:
(y-9)(y+1)

or
(x^2-9)*(x^2+1)

Which factors further into (x-3)(x+3)(x+i)(x-i)
where i is the square root of -1

Answer 3

x^4 - 8x^2 - 9
(x^2 - 9)(x^2 + 1)
(x - 3)(x + 3)(x^2 + 1)

To take this further, you would get

(x - 3)(x + 3)(x - i)(x + i)