Question : If $s-\frac{1}{s-8}=20$, then the value of $(s-8)^3-\frac{1}{(s-8)^3}$ is:
Option 1: 1324
Option 2: 1764
Option 3: 1864
Option 4: 1944
Answer (1)
24th Jan, 2024
Correct Answer: 1764
Solution :
Given: $s-\frac{1}{s-8}=20$
⇒ $s-8-\frac{1}{s-8}=12$
⇒ $(s-8-\frac{1}{s-8})^3=12^3$
⇒ $(s-8)^3-(\frac{1}{s-8})^3-3×(s-8)×\frac{1}{(s-8)}(s-8-\frac{1}{s-8})=1728$
⇒ $(s-8)^3-(\frac{1}{s-8})^3-3×12=1728$
$\therefore(s-8)^3-(\frac{1}{s-8})^3= 1764$
Hence, the correct answer is 1764.
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