欲证√[a^2+1/(a^2)]-√2>a+1/a-2,则证{√[a^2+1/(a^2)]-√2}/（a+1/a-2）>1;分子有理化,得：{(a^2+1/a^2-2)}/{（a+1/a-2）(√[a^2+1/(a^2)]+√2)}=>{(a-1/a)^2}/{（a+1/a-2）(√[a^2+1/(a^2)]+√2)}=>{(√a+1/√a)^...