∵m是方程x²-3x+1=0的一个根,
∴m²-3m+1=0,m²=3m-1,m=(3±√5)/2
(m²-2m+3)/(m²+1)
=(3m-1-2m+3)/(3m-1+1)
=(m+2)/(3m)
=(1/3)+(2/m)
=(1/3)+ 4/(3±√5)
=(1/3)+ (3-√5)或(1/3)+ (3-√5)
=(10/3) -√5,或(10/3) +√5.
题目是不是有点问题?