Question

find the value of x³+ 1/x³, if x = 2+√3

Answer 1

Answer:

It is given that , x = 2 - √3

Then 1/x = 1/(2 - √3) = (2+√3)/(4–3) = 2+√3

Now, x - 1/x = 2 - √3 - 2 - √3 = - 2√3

Therefore , x³- 1/x³

= ( x - 1/x )³+ 3 * x * 1/x ( x - 1/x )

= (- 2√3)³+ 3 ( -2√3 )

= - 24√3 - 6√3

= - 30√3