QJEEM24Macc7b: JEE Main 2024 Mathematics - Class 11 JEEM24Macc7b Solution: Let α , β be the distinct roots of the equation x 2 − ( t 2 − 5 …

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QJEEM24Macc7b: JEE Main 2024 Mathematics - Class 11 JEEM24Macc7b Solution: Let α , β be the distinct roots of the equation x 2 − ( t 2 − 5 …

Let $α, β$ be the distinct roots of the equation $x^{2} - (t^{2} - 5 t + 6) x + 1 = 0, t \in R$ and $a_{n} = α^{n} + β^{n}$ . Then the minimum value of $\frac{a_{2023} + a_{2025}}{a_{2024}}$ is

Multiple Choice Options

A −1/2
B −1/4
C `1/4
D `1/2

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Accepted Answer

$\begin{aligned} x^{2} - (t^{2} - 5 t + 6) x + 1 = 0 \\ ∴ a_{2025} - (t^{2} - 5 t + 6) a_{2024} + a_{2023} = 0 \\ \Rightarrow \frac{a_{2025} + a_{2023}}{a_{2024}} = t^{2} - 5 t + 6 \\ = {(t + \frac{5}{2})}^{2} + (\frac{- 1}{4}) \\ Minimum value = \frac{- 1}{4} \end{aligned}$

QJEEM24Macc7b: JEE Main 2024 Mathematics - Class 11 JEEM24Macc7b Solution: Let α , β be the distinct roots of the equation x 2 − ( t 2 − 5 …

Multiple Choice Options

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