Solution
Expression : $$x^2 - 3x + 1= 0$$
=> $$x^2 + 1 = 3x$$
Dividing by $$(x)$$ on both sides
=> $$x + \frac{1}{x} = 3$$
$$\because (x - \frac{1}{x})^2 = (x + \frac{1}{x})^2 - 4$$
=> $$x - \frac{1}{x} = \sqrt{9 - 4}$$
=> $$(x - \frac{1}{x}) = \pm\sqrt{5}$$
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