解一元五次方程 x^5+(20-5^(3/2))*x-(7*5^(3/2)-75)=0

风花飘飘 · 发表于 2021-12-20 08:13

本帖最后由风花飘飘于 2021-12-20 08:46 编辑

x^5+(20-5^(3/2))*x-(7*5^(3/2)-75)=0
解：
x^5+(20-5^(3/2))*x-7*5^(3/2)+75
=(x^3+((5^(1/2)))*x^2+((5^(1/2)))*x+(10-5^(3/2)))*(x^2-(5^(1/2))*x+5-5^(1/2))
=0

解：(x^3+((5^(1/2)))*x^2+((5^(1/2)))*x+(10-5^(3/2)))=0
得：x1=
x2=
x3=

解：(x^2-(5^(1/2))*x+5-5^(1/2))=0
得：x4=
x5=

风花飘飘 · 发表于 2021-12-20 08:21

本帖最后由风花飘飘于 2021-12-20 08:44 编辑

x = 1/6 (-2 sqrt(5) + 2^(2/3) (-225 + 125 sqrt(5) + 3 sqrt(30 (465 - 203 sqrt(5))))^(1/3) + (10 - 6 sqrt(5)) (2/(3 sqrt(30 (465 - 203 sqrt(5))) + 25 (5 sqrt(5) - 9)))^(1/3))
= 0.3691215649767803

x = 1/2 (sqrt(5) - i sqrt(15 - 4 sqrt(5)))

x = 1/2 (sqrt(5) + i sqrt(15 - 4 sqrt(5)))

x = 1/12 (-4 sqrt(5) + 2 (1 - i sqrt(3)) (3 sqrt(5) - 5) (2/(3 sqrt(30 (465 - 203 sqrt(5))) + 25 (5 sqrt(5) - 9)))^(1/3) - 2^(2/3) (1 + i sqrt(3)) (3 sqrt(30 (465 - 203 sqrt(5))) + 25 (5 sqrt(5) - 9))^(1/3))

x = 1/12 (-4 sqrt(5) + 2 (1 + i sqrt(3)) (3 sqrt(5) - 5) (2/(3 sqrt(30 (465 - 203 sqrt(5))) + 25 (5 sqrt(5) - 9)))^(1/3) + i 2^(2/3) (sqrt(3) + i) (3 sqrt(30 (465 - 203 sqrt(5))) + 25 (5 sqrt(5) - 9))^(1/3))

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解一元五次方程 x^5+(20-5^(3/2))x-(75^(3/2)-75)=0

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