CoCalc Shared Filessupport / 2015-03-19-203207-roots.sagews
Authors: Harald Schilly, ℏal Snyder, William A. Stein
Description: Examples for support purposes.
maxima('float(solve(7.2/(3*x-1)-3/x^2-0.6,x))')

[x=0.6125741132772068,x=2.720759220056126,x=1.0]
maxima('float(solve(7.2/(3*x-1)-3/x^2-0.64,x))')

[x=0.2901234567901235*(0.8660254037844386*%i-0.5)/(0.1081785153005215*%i+0.1127722050754458)^(1/3)+(-0.8660254037844386*%i-0.5)*(0.1081785153005215*%i+0.1127722050754458)^(1/3)+1.361111111111111,x=(0.1081785153005215*%i+0.1127722050754458)^(1/3)*(0.8660254037844386*%i-0.5)+0.2901234567901235*(-0.8660254037844386*%i-0.5)/(0.1081785153005215*%i+0.1127722050754458)^(1/3)+1.361111111111111,x=(0.1081785153005215*%i+0.1127722050754458)^(1/3)+0.2901234567901235/(0.1081785153005215*%i+0.1127722050754458)^(1/3)+1.361111111111111]
plot([7.2/(3*x-1)-3/x^2-0.6,7.2/(3*x-1)-3/x^2-0.64],(x,0.5,4))

S = solve(7.2/(3*x-1)-3/x^2-0.64, x, solution_dict=True); S

[{x: -1/2*(5/3456*I*sqrt(5591) + 10523/93312)^(1/3)*(I*sqrt(3) + 1) - 1/324*(-47*I*sqrt(3) + 47)/(5/3456*I*sqrt(5591) + 10523/93312)^(1/3) + 49/36}, {x: -1/2*(5/3456*I*sqrt(5591) + 10523/93312)^(1/3)*(-I*sqrt(3) + 1) - 1/324*(47*I*sqrt(3) + 47)/(5/3456*I*sqrt(5591) + 10523/93312)^(1/3) + 49/36}, {x: (5/3456*I*sqrt(5591) + 10523/93312)^(1/3) + 47/162/(5/3456*I*sqrt(5591) + 10523/93312)^(1/3) + 49/36}]
for soln in S:
print CDF(soln[x])

1.07509168569 + 1.11022302463e-16*I 0.604668192175 2.40357345547 - 2.77555756156e-17*I
for soln in S:
print CDF(soln[x]).real_part()

1.07509168569 0.604668192175 2.40357345547