If a - 1/(a - 4) = 11 Then find , (a - 4)3 - 1/((a - 4)^3)

Given = a - \(\frac{1}{a - 4}\) = 11

By subtracting 4 on both sides we get,

(a - 4) - \(\frac{1}{a - 4}\) = 11 - 4 = 7

(a - 4)³ - \(\frac{1}{(a - 4)^3}\) = 7³ + 3 × 7 = 364

 

Note - if x -  \(\frac{1}{x}\) = a

then x³ - \(\frac{1}{x^3}\) =  a³ + 3a