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I am trying to evaluate the following expression:

FindRoot[
  {5.813789703166071 (-(0.5/(1 - H - N1)^0.35) - 
     120000/(-120000 H + 175200000 N1)^0.35) + 
     (4.230365367527742*10^6 N2)/(H N2)^0.35 == 0, 
   5.813789703166071 (-(0.5/(1 - H - N1)^0.35) + 
     175200000/(-120000 H + 175200000 N1)^0.35) == 0, 
   10.943646979288998 (-(0.5/(1 - N2)^0.35) + 
     (386559.01232320146 H)/(H N2)^0.35) == 0}, 
  {{H, 0}, {N1, 0}, {N2, 0}}]

However, Mathematica simply returns that expression as the output without evaluating it or showing any specific error, behavior which I am not sure how to interpret even after a lot of Googling. Why is this happening?

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  • $\begingroup$ With Mathematica 11.3 (Windows 10) I get several error messages. At minimum you'll need to try other starting values as the values you give result in several of the denominators being zero. $\endgroup$ – JimB Oct 26 '18 at 20:58
  • $\begingroup$ Following @TugrulTemel 's answer: Is there some desired restriction on the roots? Are you expecting only real numbers? Should all values be between 0 and 1? $\endgroup$ – JimB Oct 26 '18 at 22:21
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Following up @JimB's comment I tried the following to show that JimB is right in his point.

FindRoot[{5.81 (-(0.5/(1 - H - N1)^0.35) - 
       120000/(-120000 H + 
           175200000 N1)^0.35) + (4.23*10^6 N2)/(H N2)^0.35 == 0, 
  5.81 (-(0.5/(1 - H - N1)^0.35) + 
      175200000/(-120000 H + 175200000 N1)^0.35) == 0, 
  10.94 (-(0.5/(1 - N2)^0.35) + (386559 H)/(H N2)^0.35) == 0}, {{H, 
   5}, {N1, 5}, {N2, 5}}]

I get the following:

FindRoot::jsing: Encountered a singular Jacobian at the point {H,N1,N2} = {1.72615*10^-9+6.11676*10^-15 I,3.5662*10^6+5.26815 I,1.7257*10^-9+3.53561*10^-15 I}. Try perturbing the initial point(s). >>

The output is:

{H -> 1.72615*10^-9 + 6.11676*10^-15 I, N1 -> 3.5662*10^6 + 5.26815 I,
  N2 -> 1.7257*10^-9 + 3.53561*10^-15 I}

The point is that as Mathematica tells us, the initial points need to be perturbed.

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