Question

plz answer me I will mark it as brainliest whoever answers first

Answer 1

Given x + 1/x = 4.

(1) 

On squaring both sides, we get

(x + 1/x)^2 = (4)^2

x^2 + 1/x^2 + 2 * x * 1/x = 16

x^2 + 1/x^2 + 2 = 16

x^2 + 1/x^2 = 16 - 2

x^2 + 1/x^2 = 14.


(2) 

(x^2 + 1/x^2) = 14

On squaring both sides, we get

(x^2 + 1/x^2)^2 = (14)^2

x^4 + 1/x^4 + 2 * x^2 * 1/x^2 = 196

x^4 + 1/x^4 + 2 = 196

x^4 + 1/x^4 = 196 - 2

x^4 + 1/x^4 = 194.



(3) 

Given (x + 1/x) = 4

On cubing both sides, we get

(x + 1/x)^3 = (4)^3

x^3 + 1/x^3 + 3 * x * 1/x * (x + 1/x) = 64

x^3 + 1/x^3 + 3 * (x + 1/x) = 64

x^3 + 1/x^3 + 3(4) = 64

x^3 + 1/x^3 + 12 = 64

x^3 + 1/x^3 = 64 - 12

x^3 + 1/x^3 = 52.



(4) 

Given (x + 1/x) = 4.


We know that (x - 1/x)^2 = (x + 1/x)^2 - 4(x)(1/x)

                                         = (4)^2 - 4

                                          = 16 - 4

                                          = 12.

 $x - \frac{1}{x} = \sqrt{12}$

$x - \frac{1}{x} = + 2 \sqrt{3} (or) -2 \sqrt{3}$



Hope this helps!