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I am trying to solve equation: x^9+p*x^4−q=0, {p, q} ∈C using functional analysis. Ηow do I solve this equation and with help Mathematica program for case p=π, q=e)? enter image description here

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  • $\begingroup$ It would be very helpful to have cut-and-pastable Mathematica InputForm. I believe this point has been made a few times now. $\endgroup$ – Daniel Lichtblau Nov 5 '18 at 20:40
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f[p_, q_, x_] = x^9 + p*x^4 - q;

sol = x /. Solve[f[Pi, E, x] == 0, x]

(* {Root[-E + π #1^4 + #1^9 &, 1], Root[-E + π #1^4 + #1^9 &, 2], 
 Root[-E + π #1^4 + #1^9 &, 3], Root[-E + π #1^4 + #1^9 &, 4], 
 Root[-E + π #1^4 + #1^9 &, 5], Root[-E + π #1^4 + #1^9 &, 6], 
 Root[-E + π #1^4 + #1^9 &, 7], Root[-E + π #1^4 + #1^9 &, 8], 
 Root[-E + π #1^4 + #1^9 &, 9]} *)

The solutions are given in terms of Root objects. The numerical values can be obtained using N

sol // N[#, 20] & // Column

enter image description here

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  • $\begingroup$ Reduce[x^9 + π*x^4 - e == 0, x] // N ,,,,,,,,=> x == 0.919688 || x == -1.08673 - 0.106027 I || x == -1.08673 + 0.106027 I || x == -0.469834 - 1.17648 I || x == -0.469834 + 1.17648 I || x == 0.050413 - 0.943033 I || x == 0.050413 + 0.943033 I || x == 1.04631 - 0.798312 I || x == 1.04631 + 0.798312 I $\endgroup$ – Nikos Mantzakouras Nov 5 '18 at 16:38
  • $\begingroup$ In your comment, e must be written as E. Built-in symbols all start with capital letters. $\endgroup$ – Bob Hanlon Nov 5 '18 at 16:42
  • $\begingroup$ The data π,e gives from Palettes of program mathematica 10 and Up $\endgroup$ – Nikos Mantzakouras Nov 5 '18 at 16:44
  • $\begingroup$ The e is in a different script. Copy and paste the code from your comment into a workbook and it will not give the desired results. $\endgroup$ – Bob Hanlon Nov 5 '18 at 16:50
  • $\begingroup$ it is not necessary in E format...I Will say again from Palettes.. $\endgroup$ – Nikos Mantzakouras Nov 5 '18 at 16:50

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