F5~續二次方程問題~3

[匿名]

2012-09-18 1:37 am

求步驟~解下列方程。

x^5-2x^3-35x=0

答案-開方7,0開方7

x^6-26x^3-27=0

答案-1,3

x^6-5x^3+4=0

答案1,3開方4

x^6-12x^4+27x^2=0

答案-3,-開方3,0,開方3,3

回答 (1)

Ka ho

2012-09-18 1:48 am

✔ 最佳答案

x^5-2x^3-35x=0
x(x^4-2x^2-35)=0
Let x^2 be y
x(y^2-2y-35)=0
x(y-7)(y+5)=0
x(x^2-7)(x^2+5)
.'.x=0 or x^2=7 or x^2=-5(rej.)
i.e. x=0 or √7 or -√7
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x^6-26x^3-27=0
Let x^3 be y
y^2-26y-27=0
(y-27)(y+1)=0
(x^3-27)(x^3+1)=0
.'. x^3=27 or x^3=-1
i.e. x=3 or -1
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x^6-12x^4+27x^2=0
x^2(x^4-12x^2+27)=0
Let x^2 be y
x^2(y^2-12y+27)=0
x^2(y-9)(y-3)=0
x^2(x^2-9)(x^2-3)=0
.'. x^2=0 or x^2=9 or x^2=3
i.e. x=0 or -3 or 3 or -√3 or √3

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