解方程组，，，，

风花飘飘

4*x^3-y*x^2+y+2=0----------------(1)
x^3+5*x-y=0-----------------------(2)

求：x，y

luyuanhong

题 解方程组 4x^3-yx^2+y+2=0 ，x^3+5x-y=0 。

解

x = 1.582035768 ，y = 11.86975677 ；

x = -0.4021023899 ，y = -2.075526410 ；

x = -1.371881783 ，y = -9.441372231 ；

x = 0.09597420203 + 1.510795358 i ， y = -0.1764290679 + 4.147330459 i ；

x = 0.09597420203 - 1.510795358 i ， y = -0.1764290679 - 4.147330459 i 。

风花飘飘

解：x^5-5*x-2=0

得：
x 1= 1.582035755478662
x 2= -0.4021023844115887
x 3=-1.371881778741866
x4 = 0.0959742020376793+1.510795358013557*i
x5 =  0.0959742020376793 -1.510795358013557*i

风花飘飘

哪个根是“共根”？
“根式”表达又是咋样的呢？

风花飘飘

x = ((sqrt(27*y^2+500)/(2*3^(3/2))+y/2)^(1/3)-5/(3*(sqrt(27*y^2+500)/(2*3^(3/2))+y/2)^(1/3)) )

风花飘飘

表达式 ：
x^5-5*x-2=0
=(4*x^3-y*x^2+y+2)*(x^3+5*x-y)
= (x^2-1)*y^2+(-x^5-8*x^3+5*x-2)*y+4*x^6+20*x^4+2*x^3+10*x
= x^2*y^2-y^2-x^5*y-8*x^3*y+5*x*y-2*y+4*x^6+20*x^4+2*x^3+10*x  
=0


解得：
(sqrt(27*y^2+500)/(2*3^(3/2))+y/2)^(1/3)-5/(3*(sqrt(27*y^2+500)/(2*3^(3/2))+y/2)^(1/3))-((3*(sqrt(27*y^2+500)/(2*3^(3/2))+y/2)^(2/3)-5)/(3*(sqrt(27*y^2+500)/(2*3^(3/2))+y/2)^(1/3)))=0
解得：
y=?