JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha, \beta\) be roots of \(x^2+\sqrt{2} x-8=0\). If \(\mathrm{U}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}\), then \(\frac{\mathrm{U}_{10}+\sqrt{2} \mathrm{U}_9}{2 \mathrm{U}_8}\) is equal to ............
- A \(5\)
- B \(9\)
- C \(44\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\( \frac{\alpha^{10}+\beta^{10}+\sqrt{2}\left(\alpha^9+\beta^9\right)}{2\left(\alpha^8+\beta^8\right)} \) \( \frac{\alpha^8\left(\alpha^2+\sqrt{2} \alpha\right)+\beta^8\left(\beta^2+\sqrt{2} \beta\right)}{2\left(\alpha^8+\beta^8\right)} \)…
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