Let S = α: log ₂(9^(2α - 4) + 13) - log ₂(5/2. 3^(2α - 4) + 1) = 2. Then the maximum value of β for which the equation x² - 2(Σ α s α)²x + Σ α s (α + 1)²β = 0 has real roots, is _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Morning shift · Q37

JEE Main 202325 Jan, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let

S = \left\{ {\alpha :{{\log }_2}({9^{2\alpha - 4}} + 13) - {{\log }_2}\left( {{5 \over 2}.\,{3^{2\alpha - 4}} + 1} \right) = 2} \right\}

. Then the maximum value of

\beta

for which the equation

{x^2} - 2{\left( {\sum\limits_{\alpha \in s} \alpha } \right)^2}x + \sum\limits_{\alpha \in s} {{{(\alpha + 1)}^2}\beta = 0}

has real roots, is ____________.

Your answerType your answer. Integers and decimals are accepted.