find the solutions. x^4+89x^2+1600=0?

Question

*****there are FOUR ANSWERS total****
pre cal prob please help.

Answer 1

use the quadratic equation

first let y=x^2

then you have y^2+89y+1600=0
y = -25, and y=-64
the final solutions are x = +/- sqrt (y)
x = 5i, -5i, 8i, -8i

Answer 2

x^4 + 89x^2 + 1600 = (X^2 + 64)(X^2 + 25) = 0

X^2 + 64 = 0 ; X^2 + 25 = 0
X^2 = -64 ; X^2 = - 25
x = +/- 8i ; x = +/- 5i

Answer 3

Take y = x^2

Then y^2 + 89y + 1600 = 0

y^2 + 25y + 64y + 64*25 = 0

y(y + 25) + 64(y + 25) = 0

(y + 64)(y + 25) = 0

y1 = -64

y2= -25

Because y=x^2

y1 = - 64 ->
x1 = +-8i

y2 = -25 ->
x2 = +-5i

Answer 4

I've decided to let MAPLE do all my work for me this morning. So, MAPLE, solve the thing for me.

>> maple('solve(x^4+89*x^2+1600=0,x)')

ans =

5*i, -5*i, 8*i, -8*i

Nice job, MAPLE. Ten point for you, good buddy.