Question

If x=2+√3 find the value of (X+1/x)^3

Answer 1

Answer:

(x + 1/x)³ = 64

Solution:

• Given : x = 2 + √3
• To find : (x + 1/x)³ = ?

We have ;

x = 2 + √3

Thus,

=> 1/x = 1/(2 + √3)

=> 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 = 2 + √3 + 2 - √3

=> x + 1/x = 4

Now,

Cubing both the sides , we get ;

=> (x + 1/x)³ = 4³

=> (x + 1/x)³ = 64

Hence,

Required answer is 64 .