x-3+1/x=0 - x+1/x = 3
(x+1/x)^2=x^2+1/x^2+2=9
x^2+1/x^2=7
(x-1/x)^2=7-2=5
所以x-1/x=正负根号5
所以x²-1/x²=(x-1/x)(x+1/x)=正负3倍根号5
已知x²－3x+1=0,求x²-1/x²的值.
x-3+1/x=0 - x+1/x = 3
(x+1/x)^2=x^2+1/x^2+2=9
x^2+1/x^2=7
(x-1/x)^2=7-2=5
所以x-1/x=正负根号5
所以x²-1/x²=(x-1/x)(x+1/x)=正负3倍根号5