NVAMediumJEE Main 2023 · 25 January, Shift 1Complex Numbers Basics

Mathematics Question from JEE Main 2023 · 25 January, Shift 1

Let S={α:log⁡2(92α−4+13)−log⁡2(52⋅32α−4+1)=2}.S = \left\{\alpha : \log_2 \left(9^{2\alpha-4} + 13\right) - \log_2 \left(\frac{5}{2} \cdot 3^{2\alpha-4} + 1\right) = 2 \right\}. Then the maximum value of β\beta for which the equation

x2−2(∑α∈Sα)2x+∑α∈S(α+1)2β=0x^2 - 2\left(\sum_{\alpha \in S} \alpha\right)^2 x + \sum_{\alpha \in S} (\alpha + 1)^2 \beta = 0

has real roots, is _____.

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