A System of Two Equations , solve x , y ?

[lvl107]

Hello Everyone.
From :

To : So the question is : "solve x , y ?"
Thanks in advance for your time and help.
Best Regards.
Loi

[Cornel]

[ttokoro · Accepted solution]

[Cornel]

Post also who is f1(x), f2(x), and how you calculate A

[lvl107]

Many thanks, Cornel, Werner, and Tokoro. And :

The query is : "Is there any approach by programming ?

Regards.

Loi.

[Werner_E]

You changed the function from tan(ln(x)) to tan(2*ln(x)) - why?

What do you mean by "calculate by hand"?

Are you aware that the system has an infinite number of solutions? Not only in the x-range from 0 to infinity, but there is also an infinite number of solution in any range from 0 to any number!

Best seen in a log-lin plot

For very small x-values the solutions are very near the zeros of the blue functions which are at x=exp(k*pi/2) where k is any integer.

[lvl107]

Best Regards.

[Werner_E]

Not that it would help in any way for a symbolic solution, but why do you state the second equation in such an unnecessarily complicated way?

Its 'simply'

The symbolic in Mathcad is not capable enough to derive that simplification (which could easily done 'by hand') but at least it can confirm that my simplification is correct