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

{√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: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

the answer would be 150 books

step-by-step explanation:

if you divide 300 by 2 you will get 150