factorise x^2+1/x^2+2-2x-2/x
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x^2+1/x^2+2-2x-2/x=0
(x+1/x)^2 - 2(x+1/x)=0
(x+1/x)(x+1/x-2)=0
x+1/x is not equal to 0
then x+1/x-2=0
x^2+1-2x=0
(x-1)^2=0
x=1
(x+1/x)^2 - 2(x+1/x)=0
(x+1/x)(x+1/x-2)=0
x+1/x is not equal to 0
then x+1/x-2=0
x^2+1-2x=0
(x-1)^2=0
x=1
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