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a difficult math question

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a difficult math question
x^2-3x+1=0,x^4+1/x^4=?,why?
From the factor,we can get that x+1/x=3
so (x+1/x)^2=x^2+1/x^2+2=9 x^2+1/x^2=7
so (x^2+1/x^2)^2=x^4+1/x^4+2=49 x^4+1/x^4=47
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