4.
The roots of the equation x2 + 16 = 4bx are real if :

b < - 2 or b > 2

Step-by-step explanation:

Given

x² + 16 = 4bx ( subtract 4bx from both sides )

x² - 4bx + 16 = 0 ← in standard form

with a = 1, b = - 4b, c = 16

For the roots to be real the discriminant b² - 4ac > 0, that is

(- 4b)² - (4 × 1 × 16) > 0

16b² - 64 > 0

16(b² - 4) > 0 ← factor using difference of squares

16(b - 2)(b + 2)  > 0, thus

b < - 2 or b > 2

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: