一不等式的证明.已知a.b.c∈R+,求证：（a/b+b/c+c/a)(b/a+c/b+a/c)≥9

Question

一不等式的证明.
已知a.b.c∈R+,求证：（a/b+b/c+c/a)(b/a+c/b+a/c)≥9

Answer 1

（a/b+b/c+c/a)≥3(a/b*b/c*c/a)^(1/3) 就是三倍的3次根号下啦,
3(a/b*b/c*c/a)^(1/3)=3
即（a/b+b/c+c/a)≥3
同理 )(b/a+c/b+a/c)≥3
有:（a/b+b/c+c/a)(b/a+c/b+a/c)≥9