verify (x+1/x)^2 - (x-1/x)^2 =4
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(x+1/x)²- (x-1/x)²=4
(x²+1+2x/x²)-(x²+1-2x/x²)=4
x²+1+2x-x²-1+2x/x²=4
4x/x² =4
4/x =4
x=4/4=1
therefore, x=1
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