If the domain of the function log ₅(18x-x²-77) is (α, β) and the domain of the function log (α-1) ((2x²+3x-2)/(x²-3x-4)) is (γ, δ), then α²+β²+γ² is equal to:

Sets, Relations and Functions: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q139

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

If the domain of the function

\log_5\left(18x-x^2-77\right)

(\alpha, \beta)

and the domain of the function

\log_{(\alpha-1)}\left(\frac{2x^2+3x-2}{x^2-3x-4}\right)

(\gamma, \delta)

, then

\alpha^2+\beta^2+\gamma^2

is equal to: