If s − 1/(s−8) =20, then the value of (s − 8)^3 −1/((s−8)^3) is:

If x - \(\frac{1}{x}\)  = n

then, $x^3 - \frac{1}{x^3}$ = n³ + 3 × n

If $s − \frac{1}{s−8} =20$

then the value of $(s − 8)^3 −\frac{1}{(s−8)^3}$ = ?

 Subtract 8 from both sides,

 $s - 8 − \frac{1}{s−8} =20 - 8$

 $s - 8 − \frac{1}{s−8} =12$

Then, $(s − 8)^3 −\frac{1}{(s−8)^3}$ =  12³ + 3 × 12

= $(s − 8)^3 −\frac{1}{(s−8)^3}$ =  1728 + 36 = 1764