WBJEE · Maths · Quadratic Equation
Let \(\alpha, \beta\) be the roots of the equation \(x^{2}-6 x-2=0\) with \(\alpha>\beta\). If \(a_{n}=\alpha^{n}-\beta^{n}\) for \(n \geq 1\), then the value of \(\frac{a_{10}-2 a_{8}}{2 a_{9}}\) is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(x^{2}-6 x-2=0\) \(x^{n}-6 x^{n-1}-2 x^{n-2}=0\) \(\Rightarrow x^{n}-2 x^{n-2}=6 x^{n-1}\) for \(n=10\) \(x^{10}-2 x^{8}=6 x^{9}\) \(\alpha^{10}-2 \alpha^{8}=6 \alpha^{9}\) \(\beta^{10}-2 \beta^{8}=6 \beta^{9}\)…
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