Question

If $x+\frac{1}{x}=2$, then $x^{16}+\frac{1}{x^{16}}$ is equal to

• A. $16$
• B. $2$
• C. $32$
• D. $24$

Answer 1

The correct option is B $2$

${\left(\begin{array}{c}x+\frac{1}{x}\end{array}\right)}^2=4$
$\Rightarrow x^2+\frac{1}{x^2}=4-2=2$
Similarly,
$\Rightarrow x^{16}+\frac{1}{x^{16}}=2$