# How can i solve this equation with solve()

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Jean Volkmar on 10 Oct 2023
Commented: Jean Volkmar on 10 Oct 2023
I want to solve this equation:
syms x
r = solve((0.02*(x-1)/(x^102 - 1))-7.59e-6,x,'ReturnConditions',true);
display(r.x)
ans =
but the r.x field does not have a solution.
syms z
z = solve((0.02*(x-1)/(x^72 - 1))-7.59e-6,x,'ReturnConditions',true);
display(double(z.x))
1.0766 + 0.0000i 1.0795 - 0.1086i 1.0795 + 0.1086i 1.0724 - 0.2081i 1.0724 + 0.2081i 1.0545 - 0.3045i 1.0545 + 0.3045i 1.0270 - 0.3982i 1.0270 + 0.3982i 0.9905 - 0.4888i 0.9905 + 0.4888i 0.9458 - 0.5756i 0.9458 + 0.5756i 0.8932 - 0.6580i 0.8932 + 0.6580i 0.8332 - 0.7353i 0.8332 + 0.7353i 0.7664 - 0.8069i 0.7664 + 0.8069i 0.6934 - 0.8724i 0.6934 + 0.8724i 0.6148 - 0.9310i 0.6148 + 0.9310i 0.5312 - 0.9825i 0.5312 + 0.9825i 0.4432 - 1.0264i 0.4432 + 1.0264i 0.3516 - 1.0623i 0.3516 + 1.0623i 0.2571 - 1.0900i 0.2571 + 1.0900i 0.1605 - 1.1092i 0.1605 + 1.1092i 0.0625 - 1.1197i 0.0625 + 1.1197i -0.0361 - 1.1216i -0.0361 + 1.1216i -0.1345 - 1.1147i -0.1345 + 1.1147i -0.2320 - 1.0992i -0.2320 + 1.0992i -0.3278 - 1.0751i -0.3278 + 1.0751i -0.4211 - 1.0426i -0.4211 + 1.0426i -0.5113 - 1.0020i -0.5113 + 1.0020i -0.5975 - 0.9535i -0.5975 + 0.9535i -0.6791 - 0.8977i -0.6791 + 0.8977i -0.7555 - 0.8348i -0.7555 + 0.8348i -0.8261 - 0.7654i -0.8261 + 0.7654i -0.8904 - 0.6901i -0.8904 + 0.6901i -0.9477 - 0.6094i -0.9477 + 0.6094i -0.9977 - 0.5239i -0.9977 + 0.5239i -1.0400 - 0.4343i -1.0400 + 0.4343i -1.0742 - 0.3414i -1.0742 + 0.3414i -1.1001 - 0.2458i -1.1001 + 0.2458i -1.1175 - 0.1482i -1.1175 + 0.1482i -1.1263 - 0.0495i -1.1263 + 0.0495i
When i change the exponent of x, i get a solution vector as i expect. I dont understand why this happens and how i can get a solution when r.x does not result in a solution vector.
Thanks for any help.

Florian Bidaud on 10 Oct 2023
Edited: Florian Bidaud on 10 Oct 2023
Solution could be using vpasolve :
syms x
r = vpasolve((0.02*(x-1)/(x^102 - 1))-7.59e-6,x);
display(r)
r =
Jean Volkmar on 10 Oct 2023
Thank you very much :)

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