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A System of Two Equations , solve x , y ?

lvl107
20-Turquoise

A System of Two Equations , solve x , y ?

Hello Everyone.
From :

I.PNG

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

1 ACCEPTED SOLUTION

Accepted Solutions
ttokoro
20-Turquoise
(To:lvl107)

7 REPLIES 7

Cornel_0-1716537797899.png

ttokoro
20-Turquoise
(To:lvl107)

image.pngimage.pngimage.pngimage.png

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

lvl107
20-Turquoise
(To:ttokoro)

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

B.PNG

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

Regards.

Loi.

Werner_E
24-Ruby V
(To:lvl107)

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

Werner_E_0-1716591885582.png

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
20-Turquoise
(To:lvl107)

C.PNG

Best Regards.

Werner_E
24-Ruby V
(To:lvl107)

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'

Werner_E_0-1716552718889.png

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

Werner_E_1-1716552907117.png

 

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