Question

解x的三次方方程 8X^3+18X^2+14X+3=0

Answer 1

用MATLAB解出来发现有1个实数根和2个虚数根。前面是解析解，后面是数值解。

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>> X=solve('8*X^3+18*X^2+14*X+3=0')

X =

((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3) - 1/(48*((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)) - 3/4

1/(96*((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)) - ((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)/2 - 3/4 - (3^(1/2)*(1/(48*((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)) + ((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3))*i)/2

1/(96*((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)) - ((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)/2 - 3/4 + (3^(1/2)*(1/(48*((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3)) + ((61^(1/2)*27648^(1/2))/27648 + 3/64)^(1/3))*i)/2

>> X=vpa(X,20)

X =

- 0.34140867674661416916

- 0.43325529665367580429*i - 0.95429566162669291542

0.43325529665367580429*i - 0.95429566162669291542