[a/根号b+b/根号a]-[根号a+根号b]
=[(a根号a+b根号b)/根号(ab)]-[(a根号b+b根号a)/根号(ab)]
=(根号a-根号b)(a-b)]/根号(ab)
=(根号a-根号b)^2(根号a+根号b)/根号(ab)≥0
∴[a/根号b+b/根号a]≥[根号a+根号b]