a/√b+b/√a
=(a√a+b√b)/(√a*√b)
=[(√a)^3+(√b)^3]/√(ab)
=(√a+√b)(a-√a√b+b)/√(ab)
>=(√a+√b)(2√a√b-√a√b)/√(ab) (a+b>=2√a√b)
=(√a+√b)(√a√b)/√(ab)
=√a+√b
证毕