x+1\x=5\2则x^3+1\x^3=_______quickly!

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x+1\x=5\2则x^3+1\x^3=_______quickly!
x+1\x=5\2则x^3+1\x^3=_______
quickly!

x+1\x=5\2则x^3+1\x^3=_______quickly!
x十1/x=5/2
两边平方
x^2十1/x^2十2=25/4
即x^2十1/x^2=17/4
两边乘以x十1/x
x^3十x十1/x十1/x^3=17/4×5/2
即x^3十1/x^3十5/2=85/8
则x^3十1/x^3=65/8

(x+1/x)^2=x^2+1/x^2+2=25/4
则x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=(5/2)*(25/4-3)=65/8

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