Question

If x= 2-root 3 then find the value of( x + 1/x)³

Answer 1

Answer:

64

Solution:

We have ;

x = 2 - √3

Thus,

1/x = 1/(2 - √3)

Now,

Rationalising the denominator in RHS , we have ;

=> 1/x = (2 + √3)/(2 - √3)(2 + √3)

=> 1/x = (2 + √3)/{2² - (√3)²}

=> 1/x = (2 + √3)/(4 - 3)

=> 1/x = (2 + √3)/1

=> 1/x = 2 + √3

Now,

=> x + 1/x = 2 - √3 + 2 + √3

=> x + 1/x = 4

=> (x + 1/x)³ = 4³

=> (x + 1/x)³ = 64

Hence,

The required value of (x + 1/x)³ is 64 .