Answer:
{√5, 10i, -10i}
Explanation:
Please use " ^ " to denote exponentiation:
x^4 + 95x^2 – 500 = 0
Temporarily substitute y for x^2:
y^2 + 95y - 500 = 0
Factor this result:
y^2 + 95y - 500 = 0 = (y + 100)(y - 5)
Set each of these factors = to 0 and solve for y:
y + 100 = 0, or y = -100. Returning to x^2 = y, we get x^2 = -100. The square root of a negative number is imaginary, so we must omit this possible answer.
y - 5 = 0 yields y = 5, and, in turn, 5 = x^2. Thus, taking only the positive root, we get x = √5.
The solution to the given equation is x = √5.
If you want the imaginary roots also, then:
Take the square root of both sides of x^2 = -100, obtaining:
x = ± i(10).
In summary, the solution set (if imaginary solutions are acceptable) is
{√5, 10i, -10i}