Question

If $x+\frac{1}{x}=3$, then the value of $x^6+\frac{1}{x^6}$ is

• A. $927$
• B. $414$
• C. $364$
• D. $322$

Answer 1

The correct option is D $322$

$x+\frac{1}{x}=3$ $\Rightarrow {(x+\frac{1}{x})}^3=3^3$
$\Rightarrow x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=27$
$\Rightarrow x^3+\frac{1}{x^3}+3\times 3=27\Rightarrow x^3+\frac{1}{x^3}=18$
${(x^3+\frac{1}{x^3})}^{}={18}^2\Rightarrow x^6+2+\frac{1}{x^6}=324$
$\Rightarrow x^6+\frac{1}{x^6}=322$