Fun Math Problem 'Cussed Ladders'

[Gerson W. Barbosa]

(09-19-2017 10:04 AM)AlexFekken Wrote:  

(09-17-2017 12:22 AM)Gerson W. Barbosa Wrote:  That's a convoluted solution, not to be taken seriously. RMollov's solution in the 2013 thread gives the distance in only one step, but its closed form version is also lengthy:

Why wouldn't you take that seriously? You get a quartic in x^2 and solving that symbolically requires using the solution of a cubic resolvent auxiliary equation (hence the cube roots). Of course a numerical solution and using explicit values for all 3 parameters avoids all that. I see no inconsistency.

The problem is mine is not a straightforward solution. If a quartic equation has to be solved, then it's better to choose RMollov's, which gives the answer we are looking for without further calculation. I don't believe my final expression, after fully simplified, would be any shorter than the one obtained through the other quartic equation.
For practical purposes it's better to use a numerical solver than those beautiful (and lengthy) exact solutions.

That's what I did then:

http://farm3.staticflickr.com/2860/11828...6eef_o.jpg

A somewhat winding road towards the desired destination.