套用公式解个简单方程，，【悬赏5万美金挑战院士填空A=？ ...

风花飘飘

32*x^5-160*x-79=0的根就是这个样子：

x1=(2*5^(1/2)+6-2*(8*(125^(1/2)+11)^2)^(1/5))
/(5*(8*(125^(1/2)+11)^2)^(1/5)-5*5^(1/2)-15)=-0.5

x2 = sqrt(15*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(1/6)/(8*sqrt(144*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(2/3)-15*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(1/3)-950))-(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(1/3)+475/(72*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(1/3))-5/24)/2+sqrt(144*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(2/3)-15*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(1/3)-950)/(24*(175*sqrt(4163)/(128*3^(3/2))+3575/3456)^(1/6))+1/8

x3=……
x4=……
x5=……

风花飘飘

科学网—套用公式解个简单方程，，【悬赏5万美金挑战院士填空A=？，B=？】 - 数学科学
://bbs.sciencenet.cn/thread-2764306-1-1.html

红树

网友………是不是开玩笑啊………钱………来者不易………

风花飘飘

{:soso_e126:} {:soso_e100:} {:soso_e146:}

风花飘飘

x^5-5*x-2=0与(5*x^3+5*x+y)*(y*x^2+20*x-y+10)=0是关于x的同解方程，我们这样来做：

把 (5*x^3+5*x+y)*(y*x^2+20*x-y+10)除以5*y后分解因式为：

(y+5*x^3+5*x)*(x^2*y-y+20*x+10)/(5*y)==(x-((sqrt(y^2-10*y+100)-10)/y))

*(x-((sqrt(27*y^2+100)/(10*3^(3/2))-y/10)^(1/3)-1/(3*(sqrt(27*y^2+100)/(10*3^(3/2))-y/10)^(1/3))))

*(x-(-(sqrt(y^2-10*y+100)+10)/y))

*(x-((-sqrt(3)*%i/2-1/2)*(sqrt(27*y^2+100)/(10*3^(3/2))-y/10)^(1/3)-(sqrt(3)*%i/2-1/2)/(3*(sqrt(27*y^2+100)/(10*3^(3/2))-y/10)^(1/3))))

*(x-((sqrt(3)*%i/2-1/2)*(sqrt(27*y^2+100)/(10*3^(3/2))-y/10)^(1/3)-(-sqrt(3)*%i/2-1/2)/(3*(sqrt(27*y^2+100)/(10*3^(3/2))-y/10)^(1/3)))) ==0

从而实现以y为待定参数的5个“根式解”。

风花飘飘

:o:o

pAq

32x^5-160^x-79=(2x+1) (16x^4-8x^3+4x^2-2x-79)=0
(2x+1)=0 ，x=-0.5
(16x^4-8x^3+4x^2-2x-79)=0  风花自己算吧。

风花飘飘

pAq 发表于 2015-9-28 10:09
32x^5-160^x-79=(2x+1) (16x^4-8x^3+4x^2-2x-79)=0
(2x+1)=0 ，x=-0.5
(16x^4-8x^3+4x^2-2x-79 ...

x1=(2*5^(1/2)+6-2*(8*(125^(1/2)+11)^2)^(1/5))
/(5*(8*(125^(1/2)+11)^2)^(1/5)-5*5^(1/2)-15)

=-0.5

风花飘飘

pAq 发表于 2015-9-28 10:09
32x^5-160^x-79=(2x+1) (16x^4-8x^3+4x^2-2x-79)=0
(2x+1)=0 ，x=-0.5
(16x^4-8x^3+4x^2-2x-79 ...

x1=(2*5^(1/2)+6-2*(8*(125^(1/2)+11)^2)^(1/5))
/(5*(8*(125^(1/2)+11)^2)^(1/5)-5*5^(1/2)-15)

=-0.5

风花飘飘