a,b,c＞ 0 ，证明：[a/(b+c)]^(2/3)+[b/(a+c)]^(2/3)+[c/(a+b)]^(2/3)≥3×4^(-1/3)

中国上海市

证明：在正数范围内[a/(b+c)]^(2/3)+[b/(a+c)]^(2/3)+[c/(a+b)]^(2/3)≥3×4^(－1/3)

波斯猫猫

提示：设f(a,b,c)=[a/(b+c)]^(2/3)+[b/(a+c)]^(2/3)+[c/(a+b)]^(2/3)，把f分别对a,b,c求导且令其为0，得到

关于a,b,c的三元方程组，解得最值点a=b=c=r(r是任意非零实数).