若x^2-5x-1=0,则x^2−1/x^2=________．

若x^2-5x-1=0,则x^2−1/x^2=________．
若x^2-5x-1=0,则x^2−1/x^2=________．

若x^2-5x-1=0,则x^2−1/x^2=________．
因为x^2-5x-1=0
所以x-1/x=5
x^2+1/x^2=27
(x+1/x)^2=29
x+1/x=正负根号28
所以x^2-1/x^2=(x+1/x)(x-1/x)=正负5倍根号29