若x^2-3x+1=0,那么x^2+1/x^2等于

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若x^2-3x+1=0,那么x^2+1/x^2等于

若x^2-3x+1=0,那么x^2+1/x^2等于
若x^2-3x+1=0,那么x^2+1/x^2等于

若x^2-3x+1=0,那么x^2+1/x^2等于
因为x^2-3x+1=0
所以x^2=3x-1
所以x^2+1/x^2
=(3x-1)+1/(3x-1)
=[(3x-1)^2+1]/(3x-1)
=(9x^2-6x+2)/(3x-1)
=[9(3x-1)-2(3x-1)]/(3x-1)
=7(3x-1)/(3x-1)
=7

x^2-3x+1=0
x-3+1/x=0,x+1/x=3
(x+1/x)^2=x^2+2+1/x^2=3^2=9
x^2+1/x^2=9-2=7
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