用换元法解一道方程 = =1-2/X-1/X^2=2X+X^2谢

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用换元法解一道方程 = =1-2/X-1/X^2=2X+X^2谢

用换元法解一道方程 = =1-2/X-1/X^2=2X+X^2谢
用换元法解一道方程 = =
1-2/X-1/X^2=2X+X^2

用换元法解一道方程 = =1-2/X-1/X^2=2X+X^2谢
1-2/x-1/x²=2x+x²
x²+1/x²+2x+2/x-1=0
(x²+1/x²)+2(x+1/x)-1=0
设x+1/x=y,则 x²+1/x²=y²-2
原方程变为 (y²-2)+2y-1=0 即y²+2y-3=0
解得y₁=-3,y₂=1
∴x+1/x=-3,或x+1/x=1
x²+3x+1=0 或x²-x+1=0
x=[-3+-根号5]/2