Question

if x- 1/x=7 , find the value of x³-1/x³​

Answer 1

$\sf{ \underline{Given : } \: \: x - \frac{1}{x} = 7 }$

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

Solution:

$\sf{ \: \: x - \frac{1}{x} = 7 }$

cubing on both sides

$\sf{ {(x - \frac{1}{x} )}^{3} = {7}^{3} }$

$\sf{ {x}^{3} - \frac{1}{ {x}^{3} } - 3(x - \frac{1}{x}) = 343 }$

$\sf{ {x}^{3} - \frac{1}{ {x}^{3} } - 3(7) = 343 }$

$\sf{ {x}^{3} - \frac{1}{ {x}^{3} } - 21= 343 }$

$\sf{ {x}^{3} - \frac{1}{ {x}^{3} } = 343 + 21 }$

$\fbox{\sf{ {x}^{3} - \frac{1}{ {x}^{3} } = 364 }}$