# Unexpected results from Solve[ ]?

Posted 5 months ago
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 HiI am having some troubles using Solve. Specifically, I want to determine the intercept curve of two surfaces. I have two functions wh[n, B] and wh1[n, B], these functions are equal for n=10^5 and B=0.32. Nevertheless, when I set B=0.32 and I use Solve to calcule the intercept point, Solve doesn’t work properly, It shows an imaginary result when It should give n=10^5. Finally, in others examples the result of Solve is { }. Would you help me with these two problems?Thank you in advance.
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Posted 5 months ago
 Thank you so much for your response!
Posted 5 months ago
 Here is an attempt. I have called (wce/wh1)==Sqrt[a] and wpe^2/wh1^2==Sqrt[b] and manipulated the equations to express a as a function of b: DivideSides[wce[B]/wh1[n, B] == Sqrt[a], wpe[n]^2/wh1[n, B]^2 == Sqrt[b], GenerateConditions -> False]; ApplySides[#^2 &, %]; MultiplySides[%, 2 e^2 n^2/(B^2 e0^2), GenerateConditions -> False]; AddSides[%, -((B^2 e^2)/m^2 + (B^2 e^2)/M^2 + (e^2 n)/(e0 m) + ( e^2 n)/(e0 M))]; ApplySides[#^2 &, %] // FullSimplify; MultiplySides[%, 1/(1/(B m M) e), GenerateConditions -> False] Solve[%, a] // FullSimplify You can check the single steps by removing the semicolons. I don't know if this is what you need.
 Solve the equation without giving numerical values to the variables: Reduce[(wh[n, B] == wh1[n, B]) && e0 > 0 && 0 < m && 0 < M && B > 0 && e > 0, Reals] You will see that the only solution in the reals can be n == 0. Still, the two functions wh and wh1 are very close in numerical value: values = {B -> 0.32, e -> 1.6*10^(-19), e0 -> 8.8*10^(-12), m -> 0.91*10^(-30), M -> 1.67*10^(-27)}; Plot[(wh[n, B] - wh1[n, B]) /. values, {n, 0, 1000000}, PlotRange -> .0001]