一元四次方程

问题描述：

一元四次方程
x^4-3X^3+4=0

答

答案是2.82201.3409-0.5815 + 0.8479i-0.5815 - 0.8479i用MATLAB求解>> solve('x^4-3*x^3+4=0') ans = 3/4+1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+1/12*((162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)-576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2)3/4+1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-1/12*((162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)-576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2) 3/4-1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+1/12*i*((-162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)+576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2) 3/4-1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-1/12*i*((-162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)+576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2)>> 3/4+1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+1/12*((162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)-576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2)ans =2.8220>> 3/4+1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-1/12*((162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)-576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2)ans =1.3409>>3/4-1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+1/12*i*((-162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)+576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2)ans =-0.5815 + 0.8479i>>3/4-1/12*3^(1/2)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)-1/12*i*((-162*(486+6*3489^(1/2))^(1/3)*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+12*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)*(486+6*3489^(1/2))^(2/3)+576*((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2)+486*3^(1/2)*(486+6*3489^(1/2))^(1/3))/(486+6*3489^(1/2))^(1/3)/((27*(486+6*3489^(1/2))^(1/3)+4*(486+6*3489^(1/2))^(2/3)+192)/(486+6*3489^(1/2))^(1/3))^(1/2))^(1/2)ans =-0.5815 - 0.8479i>>

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