Given equation is \( \Large x^{2}-3x+1=0 => x^{2}+1=3x \) = \( \Large \frac{x^{2}+1}{x}=3 \) = \( \Large \frac{x^{2}}{x}+\frac{1}{x}=3 \) Therefore, \( \Large x+\frac{1}{x}=3 \)