If a - 1/(a - 5) = 25 Then find , (a - 5)3 - 1/((a - 5)^3)

Given = a - \(\frac{1}{a - 5}\) = 25

By subtracting 5 on both sides we get,

(a - 5) - \(\frac{1}{a - 5}\) = 25 - 5 = 20

(a - 5)³ - \(\frac{1}{(a - 5)^3}\) = 20³ + 3 × 5 = 8015

 

Note - if x -  \(\frac{1}{x}\) = a

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