设x3+1/x3=2.求x+1/x

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设x3+1/x3=2.求x+1/x
设x3+1/x3=2.求x+1/x

设x3+1/x3=2.求x+1/x
x^3+1/x^3=2
x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=(x+1/x)[(x+1/x)^2-3]
x+1/x=u
u*(u^2-3)=2
u^3-3u=2
u^3+u^2-(u^2+3u+2)=0
u^2(u+1)-(u+2)(u+1)=0
(u^2-u-2)(u+1)=0
(u-2)(u+1)^2=0
u=2 或 u=-1
x+1/x=2 或x+1/x=-1

x3+1/x3=2=(x+1/x)*[(x+1/x)²-3]
t(t^2-3)=2
t=x+1/x=-1,2

(X3+1/X3)=(X+1/x)(X2-1+1/X2)=(X+1/X)((X+1/X)2-3)=2
X+1/X=2

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