【原创]】“光棍节”的“光棍数学”，很坚挺，很硬。

风花飘飘

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


x^5+2=0:
-.3549673131046296+1.092477055777454*(-1)^0.5
-.3549673131046296-1.092477055777454*(-1)^0.5
.9293164906031485-.6751879523998813*(-1)^0.5
.9293164906031486+.6751879523998813*(-1)^0.5=====(-2)^(1/5)
-1.148698354997035======-2^(1/5)

风花飘飘

方程 20*a^3*y-12*a*y^2+10*a+5=0 的解为 y
解 1
y = -(sqrt(5)*sqrt(5*a^6+6*a^2+3*a)-5*a^3)/(6*a)
解 2
y = (sqrt(5)*sqrt(5*a^6+6*a^2+3*a)+5*a^3)/(6*a)


a = (sqrt(-(1728*y^6-4320*y^4+3600*y^2-3375*y-1000)/y)/(8*15^(3/2)*y)-1/(8*y))^(1/3)+(6*y^2-5)/(30*y*(sqrt(-(1728*y^6-4320*y^4+3600*y^2-3375*y-1000)/y)/(8*15^(3/2)*y)-1/(8*y))^(1/3))

风花飘飘

【a^5-10*a^3*b^2+5*a*b^4-5*a-2=0】
【5*a^4-10*a^2*b*2+b^4-5=0】

方程 5*a^4-10*a^2*b*2+b^4-5=0 的解为 a
解 1
a1 = (-sqrt(sqrt(5)*sqrt(-b^4+20*b^2+5)+10*b)/sqrt(5) )

解 2
a2 = (sqrt(sqrt(5)*sqrt(-b^4+20*b^2+5)+10*b)/sqrt(5) )

解 3
a3= (-sqrt(10*b-sqrt(5)*sqrt(-b^4+20*b^2+5))/sqrt(5))  

解 4
a4= (sqrt(10*b-sqrt(5)*sqrt(-b^4+20*b^2+5))/sqrt(5))

红树

解题高手，五次方程进展程度怎么样了？能彻底解决吗？

风花飘飘

把x^5-5*x-2=0分解因式为：


表达式
(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))
=
((sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*(X^5+(S-R^2)*X^3-R*S*X^2-2)+(5^(3/2)+11)^(4/25)*(2^(13/25)*X^3+2^(13/25)*R*X^2+2^(13/25)*S*X)+(sqrt(5)+3)^(2/5)*(2^(12/25)*R*X-2^(12/25)*X^2))/((sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25))
=0


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


R 1= -(sqrt((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(4/25)*(4*X^6+4*S*X^4+S^2*X^2-4*X)+(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(6/25)*(2^(63/25)*X^4+2^(38/25)*S*X^2)+(sqrt(5)+3)^(3/5)*(5^(3/2)+11)^(2/25)*(-2^(62/25)*X^3-2^(37/25)*S*X)+2^(26/25)*(5^(3/2)+11)^(8/25)*X^2+2^(24/25)*(sqrt(5)+3)^(4/5))+(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*S*X-2^(13/25)*(5^(3/2)+11)^(4/25)*X-2^(12/25)*(sqrt(5)+3)^(2/5))/(2*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*X^2)


R2 = (sqrt((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(4/25)*(4*X^6+4*S*X^4+S^2*X^2-4*X)+(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(6/25)*(2^(63/25)*X^4+2^(38/25)*S*X^2)+(sqrt(5)+3)^(3/5)*(5^(3/2)+11)^(2/25)*(-2^(62/25)*X^3-2^(37/25)*S*X)+2^(26/25)*(5^(3/2)+11)^(8/25)*X^2+2^(24/25)*(sqrt(5)+3)^(4/5))-(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*S*X+2^(13/25)*(5^(3/2)+11)^(4/25)*X+2^(12/25)*(sqrt(5)+3)^(2/5))/(2*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*X^2)

风花飘飘

(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的解：

X1 = -((sqrt(5)+3)^(1/10)*sqrt((sqrt(5)+3)^(1/5)*R^2-2^(63/25)*(5^(3/2)+11)^(2/25))-(sqrt(5)+3)^(1/5)*R)/(2*(sqrt(5)+3)^(1/5))
X2=((sqrt(5)+3)^(1/10)*sqrt((sqrt(5)+3)^(1/5)*R^2-2^(63/25)*(5^(3/2)+11)^(2/25))+(sqrt(5)+3)^(1/5)*R)/(2*(sqrt(5)+3)^(1/5))
X3 = (sqrt(4*(5^(3/2)+11)^(4/25)*S^3-(5^(3/2)+11)^(4/25)*R^2*S^2+9*2^(37/25)*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*R*S-2^(62/25)*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*R^3+27*2^(24/25)*(sqrt(5)+3)^(2/5))/(2*3^(3/2)*(5^(3/2)+11)^(2/25))+((5^(3/2)+11)^(2/25)*(9*R*S-2*R^3)+27*2^(12/25)*(sqrt(5)+3)^(1/5))/(54*(5^(3/2)+11)^(2/25)))^(1/3)+(R^2-3*S)/(9*(sqrt(4*(5^(3/2)+11)^(4/25)*S^3-(5^(3/2)+11)^(4/25)*R^2*S^2+9*2^(37/25)*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*R*S-2^(62/25)*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*R^3+27*2^(24/25)*(sqrt(5)+3)^(2/5))/(2*3^(3/2)*(5^(3/2)+11)^(2/25))+((5^(3/2)+11)^(2/25)*(9*R*S-2*R^3)+27*2^(12/25)*(sqrt(5)+3)^(1/5))/(54*(5^(3/2)+11)^(2/25)))^(1/3))-R/3

风花飘飘

把x^5-5*x-2=0分解因式为：

表达式
(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))
=
((sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25)*(X^5+(S-R^2)*X^3-R*S*X^2-2)+(5^(3/2)+11)^(4/25)*(2^(13/25)*X^3+2^(13/25)*R*X^2+2^(13/25)*S*X)+(sqrt(5)+3)^(2/5)*(2^(12/25)*R*X-2^(12/25)*X^2))/((sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(2/25))
=0

R1 = -((5^(3/2)+11)^(2/25)*X^3+(5^(3/2)+11)^(2/25)*S*X-2^(12/25)*(sqrt(5)+3)^(1/5))/((5^(3/2)+11)^(2/25)*X^2)

R2= ((sqrt(5)+3)^(1/5)*X^2+2^(13/25)*(5^(3/2)+11)^(2/25))/((sqrt(5)+3)^(1/5)*X)

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

风花飘飘

把x^5-5*x-2=0分解因式为：

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

表示为；
(-((sqrt(5)+3)^(1/5)*(X^3-(((sqrt(5)+3)^(1/5)*X^2+2^(13/25)*(5^(3/2)+11)^(2/25))/((sqrt(5)+3)^(1/5)*X))*X^2)+2^(13/25)*(5^(3/2)+11)^(2/25)*X)/(sqrt(5)+3)^(1/5))
*
((X^2-(((sqrt(5)+3)^(1/5)*X^2+2^(13/25)*(5^(3/2)+11)^(2/25))/((sqrt(5)+3)^(1/5)*X))*X+(4*2^(3/5)*(5^(3/2)+11)^(2/5)/(5^(1/2)+3))^(1/5)))

风花飘飘

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

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


(X^3+R*X^2+S*X+M)*(X^2-R*X+N)
= X^5+(S-R^2+N)*X^3+(-R*S+N*R+M)*X^2+(N*S-M*R)*X+M*N
代入R、S得：
(X^3+R*X^2+S*X+M)*(X^2-R*X+N)
= -((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25)*(-X^5-N*X^3-M*X^2-M*N+2)+(sqrt(5)+3)^(3/5)*(-2^(12/25)*X^2-2^(12/25)*N)+(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(4/25)*(2^(13/25)*M-2^(13/25)*N*X)+2^(26/25)*(5^(3/2)+11)^(6/25)*X)/((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25))

= ((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25)*X^5+(sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25)*N*X^3+(sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25)*M*X^2+2^(12/25)*(sqrt(5)+3)^(3/5)*X^2+2^(13/25)*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(4/25)*N*X-2^(26/25)*(5^(3/2)+11)^(6/25)*X+(sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25)*M*N+2^(12/25)*(sqrt(5)+3)^(3/5)*N-2^(13/25)*(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(4/25)*M-2*(sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25))/((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25))

风花飘飘

(X^3+R*X^2+S*X+M)*(X^2-R*X+N)

= -((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25)*(-X^5-N*X^3-M*X^2-M*N+2)+(sqrt(5)+3)^(3/5)*(-2^(12/25)*X^2-2^(12/25)*N)+(sqrt(5)+3)^(1/5)*(5^(3/2)+11)^(4/25)*(2^(13/25)*M-2^(13/25)*N*X)+2^(26/25)*(5^(3/2)+11)^(6/25)*X)/((sqrt(5)+3)^(2/5)*(5^(3/2)+11)^(2/25))


M=((M*N)/((-N^2)^(1/5)))