问题:

不等式的证明,证明a,b,c是大于0的实数,b/(a^1/2)+c/(b^1/2)+a/(c^1/2)>=(a^1/2)+(b^1/2)+(c^1/2),麻烦勒,

更新时间:2024-04-23 21:17:41

问题描述:

不等式的证明,

证明a,b,c是大于0的实数,b/(a^1/2)+c/(b^1/2)+a/(c^1/2)>=(a^1/2)+(b^1/2)+(c^1/2),麻烦勒,

金小军回答:

  证明:∵a,b,c是大于0的实数∵b/(a^1/2)+(a^1/2)≥2(b^1/2)c/(b^1/2)+(b^1/2)≥2(c^1/2)a/(c^1/2)+(c^1/2)≥2(a^1/2)三式相加:b/(a^1/2)+c/(b^1/2)+a/(c^1/2)+(a^1/2)+(b^1/2)+(c^1/2)≥2((a^1/2)+(b^1/2)+(c^1...

最新更新