若m²-√5 m+1=0,则m-1/m=

若m²-√5 m+1=0,则m-1/m=
若m²-√5 m+1=0,则m-1/m=

若m²-√5 m+1=0,则m-1/m=
m²-√5 m+1=0
除以m
m²/m-√5 m/m+1/m=0
m+1/m=√5
(m+1/m)²=5
m²+1/m²-2=5-4
(m-1/m)²=1
m-1/m=±1

m²+1=√5m
两边平方
m^4+2m²+1=5m²
两边减去4m²
m^4-2m²+1=m²
(m²-1)²=m²
m²-1=±m
两边除以m
m-1/m=±1