Polynomial system, apparently for real champs

[boeledi]

Hi,

I have now been working for a couple of days on the following system without finding any real clue...

Could someone give me a help?
If there wouldn't be any mathematical way to solve (we never know), could someone detail me how to solve it programmatically?

In advance, many thanks

Didier

-x + y + z + 2A sin(y-z) = C
-x + y - z + 2A sin(x-z) = C
x + y - z + 2A sin(x-y) = C

where A, C are constant and A, x, y, z are not equal to 0

 

[mathwonk]

I suspect you wrote it down wrong, as it is not symmetrical, and the second equation should be x-y+z +2A sin(x-z) = C, when the solution would be x=y=z=C.

As it is, I can see no solution.

note each equation expresses one of the three letters as a single valued function of the other, (for instance the first equation is easily solved for x), so each equation could be graphed using Mathematica, and you could look at the three simultaneous graphs for a common point.

 

[M98Ranger]

Hi Didier,

Thank you for reaching out for help with your polynomial system. It sounds like you have been putting in a lot of effort without finding a solution yet.

First of all, I want to assure you that there is always a mathematical way to solve a system of equations, even if it may not be immediately obvious. However, it may require some creative thinking and using different techniques such as substitution, elimination, or graphing. It's important to not give up and continue exploring different approaches.

If you are unable to find a solution mathematically, then solving the system programmatically may be a good option. This means using a computer program or algorithm to solve the equations. There are many resources available online that can help you with this, such as mathematical software or coding forums. It would be helpful to provide more specific details about the system, such as the values of A and C, and any other relevant information.

In any case, I wish you the best of luck in solving this polynomial system. Don't hesitate to reach out for further assistance. Remember, real champs never give up!