若m²-√5 m+1=0,则m-1/m=

问题描述:

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