Express x2- 8x + 5 in the form (x -a)2-b where a and b are integers.

(x - 4)² - 11

Step-by-step explanation:

Given

x² - 8x + 5

To obtain the required form use the method of completing the square.

add/subtract ( half the coefficient of the x- term)² to x² - 8x

= x² + 2(- 4)x + 16 - 16 + 5

= (x - 4)² - 11

Step-by-step explanation:

x² - 8x + 5 = x² - 8x + (16 - 16) + 5      {we just added 16 and subtractEd it }

                 = (x - 4)² - 16 + 5               {Reason :  x² - 8x + 16 = (x - 4)² }

                 = (x - 4)² - 11

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:

b

step-by-step explanation:

the word superfluous means unnecessary