a,b,c,d>0 证(a/(b+2c+3d))+(b/(c+2d+3a))+(c/d+2a+3b))+(d/(a+2b+3c))_数学解答

a,b,c,d>0 证(a/(b+2c+3d))+(b/(c+2d+3a))+(c/d+2a+3b))+(d/(a+2b+3c))>=2/3

人气：461 ℃　时间：2019-11-16 13:06:52

解答

根据均值不等式：ab≤(a²+b²)/2ac≤(a²+c²)/2ad≤(a²+d²)/2bc≤(b²+c²)/2bd≤(b²+d²)/2cd≤(c²+d²)/2以上六式相加：ab+ac+ad+bc+bd+cd≤3(a²+b&#...