# Solve Equation trinomial Nine degree!

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)? • It would be very helpful to have cut-and-pastable Mathematica InputForm. I believe this point has been made a few times now. – Daniel Lichtblau Nov 5 '18 at 20:40

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 • 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 – Nikos Mantzakouras Nov 5 '18 at 16:38
• In your comment, e must be written as E. Built-in symbols all start with capital letters. – Bob Hanlon Nov 5 '18 at 16:42
• The data π,e gives from Palettes of program mathematica 10 and Up – Nikos Mantzakouras Nov 5 '18 at 16:44
• 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. – Bob Hanlon Nov 5 '18 at 16:50
• it is not necessary in E format...I Will say again from Palettes.. – Nikos Mantzakouras Nov 5 '18 at 16:50