Question : If $x^2+6x+1=0$, then the value of $(x+6)^3+\frac{1}{(x+6)^3}$ = ?
Option 1: 245
Option 2: 216
Option 3: 186
Option 4: 198
Correct Answer: 198
Solution : $x^2+6x+1=0$ On dividing both sides by $x$, $⇒x+6+\frac{1}{x}=0$ $⇒x+6=-\frac{1}{x}$ $⇒x=\frac{-1}{x+6}$ $⇒x+\frac{1}{x+6}=0$ Adding both sides 6. $⇒x + 6+\frac{1}{x+6}=6$ Cubing both sides of the equation Now, $(x+6)^3+\frac{1}{(x+6)^3} = 6^3-3\times 6$ $=198$ Hence, the correct answer is 198.
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