Question

its urgent please please write the answer

Answer 1

x = 2 + ∫3 , 1/x = 2-∫3
So, x + 1/x = 4
(x+1/x)3 = 43
x3 + 1/x3 + 3x + 1/x = 64
x3 + 1/x3 + 3 = 64
x3 + 1/x3 = 64 – 3 = 61

Answer 2

Given x = 2 + root 3.

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} } * \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$= \ \textgreater \ \frac{2 + \sqrt{3} }{2^2 - ( \sqrt{3} )^2}$

$= \ \textgreater \ 2 - \sqrt{3}$


Now,

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

                             = 4.



On cubing both sides, 

(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.


Hope this helps!