Let α and β be the roots of equation x2 – 6x – 2 = 0. If an = αn – βn, for n

Engineering

Mathematics

Quadratic Equation and Nature of Roots

Question

Let α and β be the roots of equation x² – 6x – 2 = 0. If an = αⁿ – βⁿ, for n > 1, then the value of $\frac{a_{10} - 2 a_{8}}{2 a_{9}}$ is equal to

–6

–3

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$\frac{a_{10} - 2 a_{8}}{2 a_{9}} = \frac{α^{8} (α^{2} - 2) - β^{8} (β^{2} - 2)}{2 (α^{9} - β^{9})} = \frac{6 (α^{9} - β^{9})}{2 (α^{9} - β^{9})} = 3$