Question

已知a＞0 b＞0 求证a／根号b+b／根号a大于等于根号a加根号b!

Answer 1

因为 a/√b+ √b≥2√[(a/√b)•√b]=2√a

b/√a+ √a≥2√[(b/√a)•√a]=2√b

相加,得 a/√b+ b/√a+√a+ √b≥2√a+2√b

即 a/√b+ b/√a≥√a+√