Question

x - ( 1 )/( x ) = sqrt ( 3 );x ^ ( 3 ) - ( 1 )/( x ^ ( 3 ) )​

Answer 1

(x-1/x)^3=x^3-1/x^3-3(x-1/x)
3(x-1/x)+(x-1/x)^2=x^3-1/^3
3root3+3=x^3-1/x^3
x^3-1/x^3=6root3

Answer 2

Answer:

6√3

Step-by-step explanation:

Given :

If $x - \frac{1}{x} = \sqrt{3}$ then,.

To find the value of : $x^3 - \frac{1}{x^3}$

Solution :

Given : $x - \frac{1}{x} = \sqrt{3}$

We know that,.

( a - b )² = a² - 2ab + b²

Substituting, a = x & b = $\frac{1}{x}$

We get,

$(x - \frac{1}{x})^2 = (\sqrt{3})^2$

⇒ $x^ 2 - 2(x)(\frac{1}{x}) + (\frac{1}{x} )^2 = 3$

⇒ $x^2 + \frac{1}{x^2} - 2 = 3$

⇒ $x^2 + \frac{1}{x^2} = 3 + 2$

⇒ $x^2 + \frac{1}{x^2} = 5$ ...(ii)

We also know that,

a³ - b³ = (a - b)(a² + ab + b²)

= $(x - \frac{1}{x})(x^2 + \frac{1}{x^2} + (x)(\frac{1}{x}))$

= $(x - \frac{1}{x})((x^2 + \frac{1}{x^2}) + 1)$

= $(\sqrt{3})(5 + 1)= 6\sqrt{3}$