Question

If x = 2 – √3, find the value of (x -1/x)cube​

Answer 1

Answer: -24√3

Step-by-step explanation:

x = 2 - √3 __(1)

Thus, 1/x = 1/(2 - √3)

Rationalising the denominator,

= (2 + √3) / [(2 - √3)(2 + √3)]

= (2 + √3) / [2² - (√3 )²]

= (2 + √3) / (4 - 3)

= 2 + √3 __(2)

Now, Subtracting eq. (1) and (2)

x - 1/x = 2 - √3 - (2 + √3)

= 2 - √3 - 2 - √3

x - 1/x = -2√3

Thus, Cubing both the sides:

(x - 1/x)³ = (- 2√3)³

(x - 1/x)³ = -24√3

Answer 2

Answer:

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