Question

Solve $x+\frac{1}{x}=3,x\ne 0$

Answer 1

$x+\frac{1}{x}=3$

$\Rightarrow x^2+1=3x$

$\Rightarrow x^2-3x+1=0$

$\Rightarrow x=\frac{-(-3)\pm \sqrt{(-3{)}^2+4(1\left)\right(1)}}{2\left(1\right)}$

$\Rightarrow x=\frac{3\pm \sqrt{5}}{2}$

$\therefore x=\frac{3+\sqrt{5}}{2}$ or $x=\frac{3-\sqrt{5}}{2}$.