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
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