If domain of the function log e ((6 x²+5 x+1)/(2 x-1))+ cos ⁻¹((2 x²-3 x+4)/(3 x-5)) is (α, β) (γ, δ], then 18(α²+β²+γ²+δ²) is equal to _ _ _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q34

JEE Main 20238 Apr, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

If domain of the function

\log _{e}\left(\frac{6 x^{2}+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^{2}-3 x+4}{3 x-5}\right)

(\alpha, \beta) \cup(\gamma, \delta]

, then

18\left(\alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2}\right)

is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.