已知a、b是正数,求证：b/√a+a√b≥√a+√b

Question

已知a、b是正数,求证：b/√a+a√b≥√a+√b

Answer 1

证明：∵a,b＞0.∴由均值不等式可得：√a+(b/√a)≥2√b,且√b+(a/√b)≥2√a.两式相加整理就得(b/√a)+(a/√b)≥√a+√b