Question

If x=2+√3, find (x+1/x)^3​

Answer 1

Answer:

Step-by-step explanation:

x=2+sqrt(3)

1/x=1/(2+sqrt(3))

rationalise the  denominator with 2-sqrt(3)

1/x=2-sqrt(3)/4-3

=2-sqrt(3)/1

=2-sqrt(3)

x+1/x=2+sqrt(3)+2-sqrt(3)=4

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

Answer 2

solution:-----

given

x = 2+√3.....................(1)

therefore

=>. 1/x= 1/ (2+√3)

= 1/(2+√3)× (2-√3) / ( 2-√3)

= ( 2-√3) / ( 4-3)

= ( 2-√3)

1/x= (2-√3)....................(2)

therefore

x+1/x= (2+√3)+(2-√3)

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

to find

value of ( x+ 1/x)³

from eqn (3)

=>. (x+1/x)³= 4³

= 64

Therefore answer is 64