Let Integral of dx/sq.rt.(e^x-1) from a to log4=pi/6. Then e^a and e^-a are the roots of equation

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Lim n tends to ♾️ [(1^2-1)(n-1)+(2^2-2)(n-2)+…+((n-1)^2-(n-1)).1]/[(1^3+2^3+…+n^3)-(1^2+2^2+…+n^2)]

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Let the maximum and minimum values of (sq.rt.(8x-x^2-12)-4)^2+(x-7)^2, x€R be M and m respectively.

Let Integral of dx/sq.rt.(e^x-1) from a to log4=pi/6. Then e^a and e^-a are the roots of equation