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Z^5+Z-1=0求Z的值
题目详情
Z^5+Z-1=0
求Z的值
求Z的值
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答案和解析
五个根分别为
1/(9*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) + ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3) - 1/3=0.7549；
1/2 + (3^(1/2)*i)/2=0.5000 + 0.8660i；
1/2 - (3^(1/2)*i)/2=0.5000 - 0.8660i；
- 1/(18*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)/2 - 1/3 + (3^(1/2)*(1/(9*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3))*i)/2=-0.8774 - 0.7449i；
- 1/(18*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)/2 - 1/3 - (3^(1/2)*(1/(9*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3))*i)/2=-0.8774 + 0.7449i；
1/(9*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) + ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3) - 1/3=0.7549；
1/2 + (3^(1/2)*i)/2=0.5000 + 0.8660i；
1/2 - (3^(1/2)*i)/2=0.5000 - 0.8660i；
- 1/(18*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)/2 - 1/3 + (3^(1/2)*(1/(9*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3))*i)/2=-0.8774 - 0.7449i；
- 1/(18*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)/2 - 1/3 - (3^(1/2)*(1/(9*((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3)) - ((23^(1/2)*108^(1/2))/108 + 25/54)^(1/3))*i)/2=-0.8774 + 0.7449i；
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