If $x^{2}-7 x+1=0$, what is the value of $\left(x+\frac{1}{x}\right) ?$

$x^{2}-7 x+1=0$

$\Rightarrow x^{2}+1=2 \sqrt{10} x$

$\Rightarrow \frac{x^{2}+1}{x}=2 \sqrt{10}$

$\Rightarrow x+\frac{1}{x}=2 \sqrt{10}$