Question

If (m-1/m) = 3, find the value of m³-1/m³​

Answer 1

⇒The trick here is to find the value of m first using the equation given.

`(m-1)/(m) =3\\m-1=m(3)\\m-1=3m\\m-3m=1\\-2m=1\\(-2m)/(-2)=(1)/(-2) \\m=-(1)/(2)`

⇒Note I used cross multiplication to solve for m

Now to find what
`(m^(3) -1)/(m^(3) )` substitute the value of m in the expression and simplify.

`=((-(1)/(2)) ^(3) -1)/((-(1)/(2) )^(3) ) \\\\=(-(1)/(8)-1 )/(-(1)/(8) ) \\=(-(9)/(8) )/(-(1)/(8) ) \\=9`

⇒The value is 9

Goodluck!!