今天求解一个三阶常系数齐次线性微分方程，要用到一元三次方程的解，所以查了一下，看到一个超强的通解公式，而且可以直接输入matlab求解，现在把它考下来，或许以后能用得着。另外还看到一元四次方程的解，不看不要紧，一看头都大了，比以前学的一元二次方程的形式复杂多了。也没验证对不对，先记下来再说。

一元三次方程：ax^3+bx^2+cx+d=0

x1=1/6/a*(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)-2/3*(3*c*a-b^2)/a/(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)-1/3*b/a


x2=-1/12/a*(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)+1/3*(3*c*a-b^2)/a/(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)-1/3*b/a+1/2*i*3^(1/2)*(1/6/a*(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)+2/3*(3*c*a-b^2)/a/(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3))


x3=-1/12/a*(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)+1/3*(3*c*a-b^2)/a/(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)-1/3*b/a-1/2*i*3^(1/2)*(1/6/a*(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3)+2/3*(3*c*a-b^2)/a/(36*c*b*a-108*d*a^2-8*b^3+12*3^(1/2)*(4*c^3*a-c^2*b^2-18*c*b*a*d+27*d^2*a^2+4*d*b^3)^(1/2)*a)^(1/3))


一元四次方程：ax^4+bx^3+cx^2+dx+e=0

x1=-1/4*b/a+1/12*3^(1/2)/a*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)+1/12/a*(-(-18*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)+48*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)+6*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-72*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)*d*b*a+288*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)*e*a^2+24*((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2)*a*c^2+144*3^(1/2)*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)*d*a^2+18*3^(1/2)*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)*b^3-72*3^(1/2)*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)*c*b*a)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)/((3*b^2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)-8*c*a*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3)+2*(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(2/3)*a-24*d*b*a+96*e*a^2+8*a*c^2)/(-36*c*b*d-288*e*c*a+108*d^2*a+108*e*b^2+8*c^3+12*(-3*b^2*d^2*c^2+240*b*d*e*a*c^2-768*e^3*a^3+384*e^2*a^2*c^2-48*e*a*c^4+81*d^4*a^2+81*e^2*b^4+576*b*d*e^2*a^2+18*b^2*d^2*e*a+12*b^3*d^3-54*c*b*d^3*a-54*c*b^3*d*e-432*e*c*a^2*d^2-432*e^2*c*a*b^2+12*d^2*a*c^3+12*e*b^2*c^3)^(1/2))^(1/3))^(1/2))^(1/2)