Recent content by edgo

OK it's some time ago, but... The connection I was referring to concerns the following. For the solutions of the equations x^7=1 and y^9=1 we can form the systems: X_1=x+\frac{1}{x} X_2=x^2+\frac{1}{x^2} X_3=x^4+\frac{1}{x^4} X_1=x^8+\frac{1}{x^8}=x+\frac{1}{x} and Y_1=y+\frac{1}{y}...

There is a very handy numerical solution for cubic equations like ## x^3+ax^2+bx+c=0## with ##x_i \in R## while a^2-3b \neq 0. Though it makes use of the method of Newton, the starting point for the algorithm gives it a great advantage to the normal algorithm. And you can use MS Excel as an...

Thanks for the advice. If x_1, x_2 and x_3 are the roots of the given equation, all FOUR conics pass through the 3 points \left(x_i,x_j\right) where i \neq j . So the COMMON points of intersection of those FOUR conics have the coordinates \left( x_i,x_j \right), that are given for this...

The following set of equations is believed to be unknown but it is very hard to become sure of that. If it is really new it might be published in Wikipedia. Does anybody know of a graphical solution of cubic equations that meets this one? I am very interested to hear from you. Given an...

Thank you for the answers. The last one is the best one and I was that far myself. Only: the shoe doesn't fit. I don't want to be a headache with my eternal questions about cube roots but the truth is that I do have a bloody good reason to be superstitious about the combination...

Just asking: is it likely that there is any connection between roots as \sqrt[3]{1} and \sqrt[7]{1}?

So it stops... so a pity. The other day there was a LaTeX editor available for this forum. I have a new laptop and lost all info about it. Please somebody can give me the necxessary information?

Thanks for the answers. Tartaglia: yes, but life isn’t fair. Let us say that Cardano is the product name. I am trying to understand the Galois related answers, simply because I am not familiar with it. I should be, but it is a long way to go just for being interested in a few answers. What I...

Thanks for your reactions. One might say that I am a believer in Galois; why not, as it is a proved theory. But my issue is a pure theoretical one and is concerning the method of solving a cubic equation. If one wants to solve a quadratic equation, he can’t avoid the presentation of quadratic...

I hope somebody will help me with the following problem. Analytical solutions of cubic equations make use of the method of Cardano. Those solutions give roots that are functions of the coefficients of the equations, being functions where cubic roots are involved. Generally speaking cubic roots...

graphical solution of the cubic with real roots Thanks Gib Z. I followed your link. I'm not sure whether Omar Khayyam solved that problem for all cubics or only for those with one real root. Wikipedia also leads to an article on Khayyam having found the generalization for all cubics with one...

Does anyone know whether the graphical solution of cubic equations with real roots by means of intersecting a circle and a parabola or hyperbola (or just a parabola and hyperbola) is known or not? That solution has to give the equations for the circles, parabolas and hyperbolas involved and not...

sorry I lost my reply on page 2. Y're welcome.

\alpha - \beta or \beta-\alpha depending on which one is the biggest

\alpha-\beta or \beta-\alpha depending on which of the two is the biggest.