Question

if x-1/x=3 then find x³-1/x³​

Answer 1

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

To find:$\:\sf{ {x}^{3} - \frac{1}{ {x}^{3} } }$

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

$\sf{{x}^{3} - \frac{1}{x^{3}} - 3(x - \frac{1}{x}) = 27}$

$\sf{{x}^{3} - \frac{1}{x^{3}} - 3(3) = 27}$

$\sf{{x}^{3} - \frac{1}{x^{3}} - 9= 27}$

$\sf{{x}^{3} - \frac{1}{x^{3}} = 27 - 9}$

$\fbox{\sf{{x}^{3} - \frac{1}{x^{3}} = 18}}$

Answer 2

Answer:

Given:\:\sf{x - \frac{1}{x} = 3}x−

x

1

=3

To find:\:\sf{ {x}^{3} - \frac{1}{ {x}^{3} } }x

3

−

x

3

1

\sf{(x - \frac{1}{x} )}^{3} = {3}^{3}(x−

x

1

)

3

=3

3

\sf{{x}^{3} - \frac{1}{x^{3}} - 3(x - \frac{1}{x}) = 27}x

3

−

x

3

1

−3(x−

x

1

)=27

\sf{{x}^{3} - \frac{1}{x^{3}} - 3(3) = 27}x

3

−

x

3

1

−3(3)=27

\sf{{x}^{3} - \frac{1}{x^{3}} - 9= 27}x

3

−

x

3

1

−9=27

\sf{{x}^{3} - \frac{1}{x^{3}} = 27 - 9}x

3

−

x

3

1

=27−9

\fbox{\sf{{x}^{3} - \frac{1}{x^{3}} = 18}}