求助elim老师：借用您的“算盘”解个4次的方程，谢谢！

风花飘飘

x^5+2=0的一个根式解的不同表达式：

x1 = -(sqrt(2^(18/25)*(11*5^(3/2)+123)^(2/25)-2^(39/25)*(sqrt(5)+3)^(1/5)*(11*5^(3/2)+123)^(1/25)+2^(2/5)*(sqrt(5)+3)^(2/5))+2^(9/25)*(11*5^(3/2)+123)^(1/25)+2^(1/5)*(sqrt(5)+3)^(1/5))/(2*(sqrt(5)+3)^(1/5))

x2= (sqrt(2^(18/25)*(11*5^(3/2)+123)^(2/25)-2^(39/25)*(sqrt(5)+3)^(1/5)*(11*5^(3/2)+123)^(1/25)+2^(2/5)*(sqrt(5)+3)^(2/5))-2^(9/25)*(11*5^(3/2)+123)^(1/25)-2^(1/5)*(sqrt(5)+3)^(1/5))/(2*(sqrt(5)+3)^(1/5))

x3= -(sqrt((11*5^(3/2)+123)^(2/25)*512^(2/25)+(sqrt(5)+3)^(1/5)*(11*5^(3/2)+123)^(1/25)*(2^(6/5)*512^(1/25)-2^(64/25))+2^(2/5)*(sqrt(5)+3)^(2/5))+(11*5^(3/2)+123)^(1/25)*512^(1/25)+2^(1/5)*(sqrt(5)+3)^(1/5))/(2*(sqrt(5)+3)^(1/5))

x4= (sqrt((11*5^(3/2)+123)^(2/25)*512^(2/25)+(sqrt(5)+3)^(1/5)*(11*5^(3/2)+123)^(1/25)*(2^(6/5)*512^(1/25)-2^(64/25))+2^(2/5)*(sqrt(5)+3)^(2/5))-(11*5^(3/2)+123)^(1/25)*512^(1/25)-2^(1/5)*(sqrt(5)+3)^(1/5))/(2*(sqrt(5)+3)^(1/5))

x5=-2^(1/5) = -1.148698354997035


x1=-1.148698354997035
x2=-1.148698354997035
x3=-1.148698354997035
x4=-1.148698354997035
x5=-2^(1/5) = -1.148698354997035

风花飘飘

(((sqrt(5)+3)^(1/5)*(x^5+2)/(2^(3/25)*(5^(3/2)+11)^(2/25)))/2^(1/5))
*
((((-2*2^(3/5)*(5^(3/2)+11)^(2/5)/(5^(1/2)+3))^(1/5))*(-2^(1/5)))/2^(1/5))
=x^5+2

风花飘飘

解下面一元二次方程，即得x^5-5*x-2=0的根：

S*X^2-R^2*X^2+(1353*5^(3/2)+15127)^(1/25)*8^(1/5)*X^2/(sqrt(5)*(11*5^(3/2)+123)^(1/5)+3*(11*5^(3/2)+123)^(1/5))^(1/5)-R*S*X+(1353*5^(3/2)+15127)^(1/25)*8^(1/5)*R*X/(sqrt(5)*(11*5^(3/2)+123)^(1/5)+3*(11*5^(3/2)+123)^(1/5))^(1/5)-(3*sqrt(5)+7)^(1/5)*65536^(1/25)*X/(sqrt(5)*(11*5^(3/2)+123)^(1/5)+3*(11*5^(3/2)+123)^(1/5))^(1/5)+(1353*5^(3/2)+15127)^(1/25)*8^(1/5)*S/(sqrt(5)*(11*5^(3/2)+123)^(1/5)+3*(11*5^(3/2)+123)^(1/5))^(1/5)+(3*sqrt(5)+7)^(1/5)*65536^(1/25)*R/(sqrt(5)*(11*5^(3/2)+123)^(1/5)+3*(11*5^(3/2)+123)^(1/5))^(1/5)+5
=0

其中：
R= ((sqrt(5)+3)^(1/5)*X^2+2^(13/25)*(5^(3/2)+11)^(2/25))/((sqrt(5)+3)^(1/5)*X)

S =(-(2*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*X^3+2^(13/25)*(5^(3/2)+11)^(4/25)*X-2^(12/25)*(sqrt(5)+3)^(2/5))/((sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*X))