Let α, β be roots of x² + √2x − 8 = 0. If Uₙ = αⁿ + βⁿ, then U_ 10 + 2U_9 2U_8 is equal to _____.

JEE Main 2024 Mathematics question

Let α, β be roots of x² + √2x − 8 = 0. If Uₙ = αⁿ + βⁿ, then is equal to .

Answer: 4

Since αⁿ⁺² = −√2αⁿ⁺¹ + 8αⁿ, Uₙ₊₂ + √2Uₙ₊₁ = 8Uₙ. So (U₁₀ + √2U₉)/(2U₈) = 8U₈/(2U₈) = 4. (The

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Question ID VK-012145