Question

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.

Answer 1

Answer:

{√5, 10i, -10i}

Step-by-step 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}

Answer 2

Answer:

In order to calculate x you need to revers the sides as below

x4 = 500 - (95x2)

x4 = 500 -190

x4 = 310

x = 310/4

x = 77.5

Step-by-step explanation: