Question

设a,b,c是方程x^3+px+q=0 的三个根,行列式 a b c

Answer 1

x1=1/6*(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)-2*p/(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)

x2=-1/12*(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)+p/(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)+1/2*i*3^(1/2)*(1/6*(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)+2*p/(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3))

x3=-1/12*(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)+p/(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)-1/2*i*3^(1/2)*(1/6*(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3)+2*p/(-108*q+12*(12*p^3+81*q^2)^(1/2))^(1/3))