Mathematician Finds Easier Way to Solve Quadratic Equations

[Namir]

(05-02-2024 02:00 PM)Albert Chan Wrote:  

(05-01-2024 11:08 PM)Gerson W. Barbosa Wrote:  \(x_{1,2}=\sqrt{q}\times e^{±\cosh^{-1}{(-\frac{p}{2\sqrt{q}}})}\)

exp/cosh quadratic formula avoided subtraction canellation, but introduced another.
Exponential function slope is also an exponential function!

e^(x*(1-ε)) ≈ e^x - (x*e^x)*ε

RelErr(x) = ε      ⇒ RelErr(e^x) = (exact - approx) / exact ≈ (x*e^x)*ε / e^x = x*ε

Interesting formula but it uses more CPU power to calculate invers cosh and exp(x) in addition to the square root!

Namir