用换元法解分式方程(x-2/x)^2-2x+4/x=-1

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用换元法解分式方程(x-2/x)^2-2x+4/x=-1
用换元法解分式方程(x-2/x)^2-2x+4/x=-1

用换元法解分式方程(x-2/x)^2-2x+4/x=-1
令x-2/x=t,则t^2-2t+1=0,t=1,所以x-2/x=1,即x^2-x-2=0,解得x=2,或x=-1

(x-2/x)^2-2*(x-2/x)=-1;
令t=x-2/x,
t^2-2t+1=0,t=1,
x-2/x=1,x^2-x-2=(x-2)(x+1)=0,x1=2,x2=-1

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