Question

已知x²-3x+1=0 求根号下(x²)+1/x²-2的值

Answer 1

x^2-3x+1=0
因为x=0不是方程的解，所以方程两边可以同时除以x
x-3+1/x=0
x+1/x=3
x^2+1/x^2=(x+1/x)^2-2=3^2-2=7
根号下(x2)+1/x2-2=根号下(7-2)=根号5

Answer 2

∵x²-3x+1=0
∴方程两边同除以x
得x-3+1/x=0
x+1/x=3
∴（x+1/x）²=x²+2+1/x²=3²=9
即x²+1/x²=9-2=7
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原式=√x²+1/x²-2
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=
√7-2
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=√5