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
Answer (1)
16th Jan, 2024
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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