(HP-67) Barkers's Equation

[Albert Chan]

Welcome to the forum, Mathias Zechmeister

Hyperbolic solutions to the cubics is simply matching hyperbolic triple angle formula.
see https://mathworld.wolfram.com/CubicFormula.html, eqn 78,79,80

(12-06-2019 06:39 PM)Albert Chan Wrote:  Solving cubic with Cardano's formula, x³ + 3x - 2W = 0

y = ³√(W + √(W²+1))
x = y - 1/y

Another way is with identity: sinh^-1(z) = ln(z + √(z²+1))
→ y = e^(sinh^-1(W)/3)
→ x = 2 sinh(sinh^-1(W)/3)