0
$\begingroup$

I am trying to solve those equations:

eqns = 
  -1796853 + 19321 x + 83018.53984692502` x (-8649 + x^2) + 
      39.56247732409712` x (-8649 + x^2)^2 + 
      0.005059047659697752` x (-8649 + x^2)^3 + 
      10.329634791516803` x ((1000 + 
            1.7850911998308758` y) Sqrt[-101.94940899999999` x^2 + \
(1000 + 1.7850911998308758` y)^2] - 
         101.94940899999999` x^2 Log[(
           0.09903931860948798` (1000 + 1.7850911998308758` y + 
              Sqrt[-101.94940899999999` x^2 + (1000 + 
                 1.7850911998308758` y)^2]))/x]) == 0 && 
    611524 y + 
      0.1205783688509235` (-101.94940899999999` x^2 + (1000 + 
           1.7850911998308758` y)^2)^(3/2) == 0 // Simplify;

I have already used some conditions to avoid for negative values inside the Log function as indicated on another post How to solve this system with logarithms? but it did not work for my case:

cons = 
  And @@ Cases[eqns, Log[z_] :> z > 0, Infinity] // 
    Simplify[#, Element[{x, y}, Reals]] &

sol = NSolve[eqns && cons, {x, y}, Reals]

It just returns me the NSolve function without solving it.

Any help will be appreciated.

Improve this question
$\endgroup$
3
  • 2
    $\begingroup$ NMinimize[Abs[expr1]+Abs[expr2],{x,y}] finds a small minimum but logargument/.solution is negative. NMinimize[{Abs[expr1]+Abs[expr2],logargument>0},{x,y}] finds a huge minimum but logargument/.solution is positive. Is it possible there is no solution for positive logargument? $\endgroup$
    – Bill
    Commented Dec 5, 2020 at 23:20
  • $\begingroup$ I'll investigate what you pointed out, maybe I made some mistake in deriving those eqs (physical solutions in the model I'm working with require for positive logargument). On the other hand I expect that NSolve response for the case of no solutions to be the empty set "{}". Thank you Bill. $\endgroup$
    – Rodrigo Da Mata
    Commented Dec 6, 2020 at 0:58
  • $\begingroup$ Your "cons" defines a function, but it is used without argument. $\endgroup$
    – Daniel Huber
    Commented Dec 6, 2020 at 8:57

1 Answer 1

Reset to default
0
$\begingroup$ 
Clear["Global`"]

eqns = -1796853 + 19321 x + 83018.53984692502` x (-8649 + x^2) + 
       39.56247732409712` x (-8649 + x^2)^2 + 
       0.005059047659697752` x (-8649 + x^2)^3 + 
       10.329634791516803` x ((1000 + 
             1.7850911998308758` y) Sqrt[-101.94940899999999` x^2 + \
(1000 + 1.7850911998308758` y)^2] - 
          101.94940899999999` x^2 Log[(0.09903931860948798` (1000 + 
                 1.7850911998308758` y + 
                 Sqrt[-101.94940899999999` x^2 + (1000 + 
                    1.7850911998308758` y)^2]))/x]) == 0 && 
     611524 y + 
       0.1205783688509235` (-101.94940899999999` x^2 + (1000 + 
              1.7850911998308758` y)^2)^(3/2) == 0 // 
    Rationalize[#, 0] & // Simplify;

ContourPlot[Evaluate[List @@ eqns], {x, -100, 100}, {y, -120, 40}]

enter image description here

sol = FindRoot[eqns, {x, 95}, {y, -10}, WorkingPrecision -> 20]

(* {x -> 92.986023667945379060, y -> -5.9811971865340859795} *)

eqns /. sol

(* True *)
Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you for your attention Bob. $\endgroup$
    – Rodrigo Da Mata
    Commented Dec 7, 2020 at 19:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.