一道数学题

显示全部楼层 · 2013-8-8 18:52:30

Solve[x^3 + x + 1 == 0, x]{{x -> -(2/(3 (-9 + Sqrt[93])))^(1/3) + (1/2 (-9 + Sqrt[93]))^(1/3)/
3^(2/3)}, {x -> -(((1 + I Sqrt[3]) (1/2 (-9 + Sqrt[93]))^(1/3))/(
2 3^(2/3))) + (1 - I Sqrt[3])/(
2^(2/3) (3 (-9 + Sqrt[93]))^(
1/3))}, {x -> -(((...

千问 · 2013-8-8 18:52:30

存在唯一的x使x3+x+1的值为0http://baike.baidu.com/view/1125876.htm...

千问 · 2013-8-8 18:52:30

先设x=y-1/3y代入得y^3-1/(27y∧3)+1=0再设y^3=w化为w-1/(27w)+1=0∴w^2+w-1/27二0解出w=(-1±根号(31/27)/2再解出y，解出x，自己再算一下x很复杂，我给出x近似值，x≈-0、682327803，核对一下望采纳，不懂再来问吧...