求证:a^5/b^3c^3+b^5/c^3a^3+c^5/a^3b^3≥1/a+1/b+1/c
问题描述：
求证:a^5/b^3c^3+b^5/c^3a^3+c^5/a^3b^3≥1/a+1/b+1/c
用排序不等式解下谢谢!
答
设a>=b>=c, S = a^5/b^3c^3+b^5/c^3a^3+c^5/a^3b^3(感觉少了个a,b,c都大于0的条件）于是有1/b^3c^3 >= 1/c^3a^3 >= 1/a^3b^3, a^5 >= b^5 >= c^5S = a^5 * (1/b^3c^3) + b^5* (1/c^3a^3) + c^5* (1/a^3b^3) >=...