SOLVE x^4 − 15x^2 − 16 = 0
What are the roots of the equation?

roots : 4, -4, i, -i

Step-by-step explanation:

This gets a bit tricky.

We have to substitude x^2 as u in this problem.

Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get

u^2 - 15u - 16 = 0

( u - 16) (u + 1)

U = 16

U = -1

This is not the end of the problem.

Now we have to substitute x^2 back to u.

x^2 = 16  --> we get the roots 4 and -4

x^2 = -1 --> we get the roots i and -i

tadah!

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

19

step-by-step explanation: