Y=a2+1/a2-(a+1/a)=(a+1/a)^2-(a+1/a)-2
令x＝a+1/a可知X≥2或X≤－2
Y＝X＾2－X－2
令Y＝0得X＝2或X＝－1
故当X≥2时,Y≥0即a2+1/a2≥a+1/a
　当X≤2时,Y≥0即a2+1/a2≥a+1/a
故a≠0时,总有a2+1/a2≥a+1/a,a=0时等号成立