HP50g simplifing a root

[Albert Chan]

(10-09-2020 02:31 PM)Albert Chan Wrote:  Lets rearrange the cubic to match form x³ + 3px - 2q = 0

c³ = A² - R
4*a³ = 3*c*a + A
a³ + 3*(-c/4)*a - 2*(A/8) = 0

→ Cubic discriminant = p³ + q² = (-c/4)³ + (A/8)² = (-c³ + A²) / 64 = R/64
→ If R < 0, we got 3 real roots.

see https://proofwiki.org/wiki/Cardano%27s_Formula

I just realized my direct calculation for a is really using Cardano's formula

a = ³√(q + √Δ) + ³√(q - √Δ)
   = ³√((A/8) + √(R/64)) + ³√((A/8) - √(R/64))
   = (³√(A+√R) + ³√(A-√R)) / 2