3 ms·

α⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0 α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.

α⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0 α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.66...)/(6577.74...) α = (24 + 117.12...)/(6577.74...) α = 141.12.../6577.74... α ≈ 0.021454... α⁻¹ ≈ 46.61 ??? That's wrong!

albert_roca 10mo ago
You transcribed the formula incorrectly. The term is -(alpha / 24). You calculated -1 / (24 · alpha). The correct derivation is: 1 / alpha = S - (alpha / 24) 1 = S · alpha - (alpha^2) / 24 alpha^2 - 24 · S · alpha + 24 = 0 Solving this with S = 4 · π^3 + π^2 + π yields the correct value.