已知a>0,求证：√(a^2+1/a^2)-√2≥a+1/a-2.∵1/[( 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) -√(a^2+1/a^2)]}=[( a+1/a) +√(a^2+1/a^2)] /{[( a+1/a)^2-(a^2+1/a...