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\[\frac{a_{10} - 2a_{8}}{2a_{9}}\] = \[\frac{(\alpha^{10} - \beta^{10}) - 2(\alpha^{8} - \beta^{8})}{2(\alpha^{9} - \beta^{9})}\]
= \[\frac{\alpha^{8}(\alpha^{2} - 2) - \beta^{8}(\beta^{2} - 2)}{2(\alpha^{9} - \beta^{9})}\]
∵𝛼 is root of x² - 6x - 2 = 0 ⇒ 𝛼² - 2 = 6𝛼
[ and β is root of x² - 6x - 2 = 0 ⇒ ꞵ² - 2 = 6ꞵ]
= \[\frac{\alpha^{8}(6\alpha) - \beta^{8}(6\beta)}{2(\alpha^{9} - \beta^{9})} = \frac{6(\alpha^{9} - \beta^{9})}{2(\alpha^{9} - \beta^{9})}\] = 3
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