已知:x²-7x+1=0,求x-1/x

已知:x²-7x+1=0,求x-1/x
已知:x²-7x+1=0,求x-1/x

已知:x²-7x+1=0,求x-1/x
x²-7x+1=0 (两边同时除以x,x≠0)
x-7+1/x=0
(x+1/x)=7
(x+1/x)^2=49
(x-1/x)^2=(x+1/x)^2-(4*x*(1/x))=49-4=45
所以
x-1/x=±√45=±3√5(x≠0)