【原创]】“光棍节”的“光棍数学”，很坚挺，很硬。

风花飘飘

把x^5-5*x-2=0分解

因式为：
(X^3+R*X^2+S*X+(-2/(4*2^(3/5)*(5^(3/2)+11)^(2/5)/(5^(1/2)+3))^(1/5)))
*
(X^2-R*X+(4*2^(3/5)*(5^(3/2)+11)^(2/5)/(5^(1/2)+3))^(1/5))
=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))

风花飘飘

红树

已知：a>0，b>0，m>0，n>0，a≠b≠m≠n，a，b，m，n满足方程a^2+b^2=m^2+n^2，2a+b=2m+n
求a=?，b=?，m=?，n=?，是否能找到一组解，

风花飘飘

红树 发表于 2015-6-30 14:36
已知：a>0，b>0，m>0，n>0，a≠b≠m≠n，a，b，m，n满足方程a^2+b^2=m^2+n^2，2a+b=2m+n
求a=?，b=?，m=? ...

这种小题，不要在大题的后面跟帖，最好单独发帖，免的破坏大题帖子的完美。
告诉你答案：

a = (4*n+3*m)/5
b = -(3*n-4*m)/5

注：m、n取值勾股三角形的两条直角边。

红树

a = (4*n+3*m)/5
b = -(3*n-4*m)/5
负号带表什么？没有看懂，没有求出m和n值？

红树

是否能给出一个例？

风花飘飘

伽罗瓦解不出来的方程x^5-5*x-2=0

我们可以通过解这个方程组来求解：

x^3+5*x-y=0----------------------------(1)
4*x^3-y*x^2+y+2=0------------------(2)
消去x，求出y来，代入(1)、(2)，再通过解这两个3次方程而求出x^5-5*x-2=0的根来。（这两个3次方程有一个“共根”）

共根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))

其中
y=
((45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)-28*3^(1/6)*5^(1/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-5501*3^(1/3)*5^(1/3))/(2*3^(7/6)*5^(7/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))


x1 = (sqrt(3^(5/3)*5^(5/3)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(4/3)+1450950*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)+308056*3^(13/6)*5^(13/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-56*3^(11/6)*5^(11/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))+30261001*3^(7/3)*5^(7/3))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))-((-3^(5/6)*5^(5/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3))+420*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)+5501*3^(7/6)*5^(7/6))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)))^(1/3)*((-1/2)-(sqrt(3)*%i)/2)-(5*((sqrt(3)*%i)/2-1/2))/(3*(sqrt(3^(5/3)*5^(5/3)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(4/3)+1450950*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)+308056*3^(13/6)*5^(13/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-56*3^(11/6)*5^(11/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))+30261001*3^(7/3)*5^(7/3))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))-((-3^(5/6)*5^(5/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3))+420*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)+5501*3^(7/6)*5^(7/6))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)))^(1/3))

x2 = (sqrt(3^(5/3)*5^(5/3)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(4/3)+1450950*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)+308056*3^(13/6)*5^(13/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-56*3^(11/6)*5^(11/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))+30261001*3^(7/3)*5^(7/3))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))-((-3^(5/6)*5^(5/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3))+420*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)+5501*3^(7/6)*5^(7/6))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)))^(1/3)*((sqrt(3)*%i)/2-1/2)-(5*((-(sqrt(3)*%i)/2)-1/2))/(3*(sqrt(3^(5/3)*5^(5/3)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(4/3)+1450950*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)+308056*3^(13/6)*5^(13/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-56*3^(11/6)*5^(11/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))+30261001*3^(7/3)*5^(7/3))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))-((-3^(5/6)*5^(5/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3))+420*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)+5501*3^(7/6)*5^(7/6))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)))^(1/3))

x3 = (sqrt(3^(5/3)*5^(5/3)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(4/3)+1450950*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)+308056*3^(13/6)*5^(13/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-56*3^(11/6)*5^(11/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))+30261001*3^(7/3)*5^(7/3))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))-((-3^(5/6)*5^(5/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3))+420*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)+5501*3^(7/6)*5^(7/6))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)))^(1/3)-5/(3*(sqrt(3^(5/3)*5^(5/3)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(4/3)+1450950*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3)+308056*3^(13/6)*5^(13/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)-56*3^(11/6)*5^(11/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))+30261001*3^(7/3)*5^(7/3))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3))-((-3^(5/6)*5^(5/6)*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(2/3))+420*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)+5501*3^(7/6)*5^(7/6))/(900*(45*sqrt(2203)*sqrt(859913)-298792*sqrt(3)*sqrt(5))^(1/3)))^(1/3))

风花飘飘

2^(3/5)*(47+21*sqrt(5))^(1/5)*X^4+2^(44/25)*(3+sqrt(5))^(1/5)*(7+3*sqrt(5))^(1/5)*(123+11*5^(3/2))^(1/25)*X^2-2^(3/5)*(9+4*sqrt(5))^(1/5)*X^2+2^(34/25)*(7+3*sqrt(5))^(1/5)*(15127+1353*5^(3/2))^(1/25)-2^(19/25)*(7+3*sqrt(5))^(1/5)*(123+11*5^(3/2))^(1/25)
=0
的解？

风花飘飘

波浪

还算捞起几个帖子，建议大家一起捞。