设a,b,c,d为不全相等的正数,求证:(1⼀a+b+c)+(1⼀b+c+d)+(1⼀c+d+a)+(1⼀d+a+b)>16⼀3(a+b+c+d)

2025-03-01 12:35:51
推荐回答(1个)
回答1:

(1/(a+b+c)+1/(b+c+d)+1/(c+d+a)+1/(d+a+b))*((a+b+c)+(b+c+d)+(c+d+a)+(d+a+b))>16
所以1/(a+b+c)+1/(b+c+d)+1/(c+d+a)+1/(d+a+b)>16/3(a+b+c+d)
(利用柯西不等式)