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# Why Mathematica Can't Solve this Equation

Posted 10 years ago
 I have tries to solve an equation by using Solve[] to find pl as a function of other variables. However, it generates an Error! Can anyone help? In[780]:= ClearAll["Global*"] Clear[temp] temp = Solve[(((1 - pi)*(pl - ph)/(1 - ph))^((1 - pi)*\[Lambda]l))*((pi*(pl - ph)/(pl - 1))^(pi)) == ((pi*(pl - ph)*R/(ph*(pl - 1)))^(pi*(1 - \[Lambda]h)))*(((pl - ph)*(pi*\[Lambda]h + \[Lambda]l - pi*\[Lambda]l)/(\[Lambda]h*(pl - 1) + \[Lambda]l*(1 - ph)))^(pi*\[Lambda]h + \[Lambda]l - pi*\[Lambda]l)),{pl}] During evaluation of In[780]:= Solve::nsmet: This system cannot be solved with the methods available to Solve. >> Out[782]= Solve[(((1 - pi) (-ph + pl))/(1 - ph))^((1 - pi) \[Lambda]l) ((pi (-ph + pl))/(-1 + pl))^pi == ((pi (-ph + pl) R)/(ph (-1 + pl)))^(pi (1 - \[Lambda]h)) (((-ph + pl) (pi \[Lambda]h + \[Lambda]l - pi \[Lambda]l))/((-1 + pl) \[Lambda]h + (1 - ph) \[Lambda]l))^(pi \[Lambda]h + \[Lambda]l - pi \[Lambda]l), {pl}]  Attachments:
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Posted 10 years ago
 Sometimes NMinimize of the Norm of an expression with some constraints NMinimize[{Norm[ (((1 - pi)*(pl - ph)/(1 - ph))^((1 - pi)*\[Lambda]l))*((pi*(pl - ph)/(pl - 1))^(pi)) - ((pi*(pl - ph)* R/(ph*(pl - 1)))^(pi*(1 - \[Lambda]h)))*(((pl - ph)*(pi*\[Lambda]h + \[Lambda]l - pi*\[Lambda]l)/ (\[Lambda]h*(pl - 1) + \[Lambda]l*(1 - ph)))^(pi*\[Lambda]h + \[Lambda]l - pi*\[Lambda]l))], 0<=pi<=1 && 0<=\[Lambda]h<=1 && 0<=\[Lambda]l<=1 && 1<=R<=2 && 0<=ph<=1 && 1<=pl<=2}, {pi, \[Lambda]h, \[Lambda]l, R, ph, pl}] can find solutions.In this case it also complains about some things that you might think carefully about.
Posted 10 years ago
 Sorry, I should also mention that; 0 <= pi <= 1 && 0 <= \[Lambda]h <= 1 && 0 <= \[Lambda]l <= 1 && 1 <= R <= 2 && 0 <= ph <= 1 && 1 <= pl <= 2 `Thanks!!!
Posted 10 years ago
 Thank you very much Bill. I am just wondering would it be possible to get closed-form solution in this case?
Posted 10 years ago
 I doubt it.