Question

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

• A. 927
• B. 114
• C. 364
• D. 322

Answer 1

Answer: (D)

322

$x+\frac{1}{x}=3$
$x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=27$
$x^3+\frac{1}{x^3}=27-9=18$
$(x^3+\frac{1}{x^3}{)}^2=(x^6+\frac{1}{x^6}+2)$
Now, $x^6+\frac{1}{x^6}+2=324$
$x^6+\frac{1}{x^6}=322$