Question

12. If x = 2 – √3, find the value of (x – 1/x)^3​

Answer 1

Answer:

X=2-√3

=>1/x = 1/(2-√3)

=>1/x=2+√3

Now,

x-(1/x)=(2-√3)-(2+√3)

=>x-(1/x)=-2√3

=>{x-(1/x)} ³=-24√3

Answer 2

Answér :

(x - 1/x)³ = -24√3

Solution :

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

We have ;

x = 2 - √3

Thus ,

1/x = 1/(2 - √3)

Now ,

Rationalising the denominator of the term in RHS , we get ;

=> 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 = -2√3

Now ,

Cubing both the sides , we get ;

=> (x - 1/x)³ = (-2√3)³

=> (x - 1/x)³ = -24√3

Hence ,

(x - 1/x)³ = -24√3