If \( \alpha \) and \( \beta (\alpha < \beta) \) are the roots of the equation \( (-2 + \sqrt{3})\lvert \sqrt{x} - 3 \rvert + (x - 6\sqrt{x}) + (9 - 2\sqrt{3}) = 0, \ \ x \ge 0 \), then \( \sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha \beta} \) is equal to:
