Question

If $x+\frac{1}{x}=3$, then $x^3+\frac{1}{x^3}$ is

• A. $9$
• B. $18$
• C. $27$
• D. $6$

Answer 1

The correct option is B $18$

$x+\frac{1}{x}=3$
${(x+\frac{1}{x})}^3=x^3+\frac{1}{x^3}+3(x+\frac{1}{x})$
or $3^3=x^3+\frac{1}{x^3}+3\times 3$
or $27=x^3+\frac{1}{x^3}+9$
$\therefore x^3+\frac{1}{x^3}=27-9=18$