求简便算法If x2 - 3x + 1 = 0, what is the value of x2 + (1/x)2 ?

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求简便算法If x2 - 3x + 1 = 0, what is the value of x2 + (1/x)2 ?
A. 7 B. (7 −3√5 )/2 C. 9 D. (7 +3√5 )/2 E. 10
求简便算法,直接算实在是繁琐,应该还有其他解法

x^2-3x+1=0
显然 x不等于0
这样
x^2+1=3x
两边同除以x有：
x+1/x=3
再两边平方,有：
x^2+1/x^2+2=9
所以 x^2+(1/x)^2=9-2=7
选A

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