If `x-1/x=5` , find the value of `x^3-1/(x^3)`

Explanation

Given,
`x− 1/x=5`
Squaring both the sides,`=(x− 1/x )^2 =5^2`
`=x^2+ 1/x^2 −2(x)( 1/x )=25`
`=x^2 + 1/x^2 =25+2`
`=x^2 + 1/x^2 =27`
Now,
`x^3− 1/x^3`
`=(x− 1/x )[(x)^2+(1/x )^2 +(x)( 1/x )]`
`=5(27+1)`
`=140`