不等式左边=[a+1/a-√(a^2+1/a^2)]*[[a+1/a+√(a^2+1/a^2)]]/[a+1/a+√(a^2+1/a^2)] =[(a+1/a)^2-(a^2+1/a^2)]/[a+1/a+√(a^2+1/a^2)] =2/[a+1/a+√(a^2+1/a^2)] 而显然a+1/a>=2,a^2+1/a^2>=2 所以上式<=2/(2+√2)=2-√2 当且仅当a=1时等号成立
