Question

if x=2-root3 find the value of (x-1/x)³​

Answer 1

Answer:

- 30√3

Step-by-step explanation:

x = 2 - √3 → 1/x = 1/(2 - √3)

Multiply and divide RHS by 2 + √3:

=> 1/x = 1/(2 - √3) × (2 + √3)/(2 + √3)

=> 1/x = (2 + √3)/(2 - √3)(2 + √3)

=> 1/x = (2 + √3)/(2² - √3²)

=> 1/x= (2 + √3)/(4 - 3)

=> 1/x = 2 + √3

Thus,

x - 1/x = 2 - √3 - (2 + √3)

x - 1/x = - 2√3

Cube on both sides,

=> x³ - 1/x³ - 3(x*1/x)(x - 1/x) = - 24√3

=> x³ - 1/x³ - 3(1)(-2√3) = - 24√3

=> x³ - 1/x³ = - 24√3 - 6√3

=> x³ - 1/x³ = - 30√3