Question

a b c都为正实数 根号下a/(b+c)加根号下b/(a+c)加根号下c/(a+b)大于2 怎么证明啊

Answer 1

∵√[a/(b+c)]=√[a²/(a(b+c))]=a/√[a(b+c)]

又 √[a(b+c)]≤(a+b+c)/2 （均值）

∴√[a/(b+c)]≥2a/(a+b+c)

同√[b/(a+c)]≥2b/(a+b+c)

√[c/(a+b)]≥2c/(a+b+c)

3式不同等,加取>右为2,自己来哈