m^2-√10m+1=0,求m^4+m^(-4).

m^2-√10m+1=0,求m^4+m^(-4).
m^2-√10m+1=0,求m^4+m^(-4).

m^2-√10m+1=0,求m^4+m^(-4).
m^2+1=√10m
m^4+m^(-4)=(m^2+1/m^2)^2-2=[(m+1/m)^2-2]^2-2=(m+1/m)^4+4-4(m+1/m)^2-2=(m+1/m)^4-4(m+1/m)^2+2
m+1/m=(m^2+1)m=√10,代入得
100-40+2=62

m^2-√10m+1=0
m+1/m=√10
m^4+1/m^4
=(m^2+1/m^2)-2
=(m+1/m)^2-4
=10-4
=6