Given that a,b,c >0
Prove : (a/b + b/c +c/a)(b/a +c/b +a/c)>0
multiply them out. just starting with term by term, one gets
1+1+1+.... and since the remaining terms are non negative, or >0, then the sum must be >0
Prove : (a/b + b/c +c/a)(b/a +c/b +a/c)>0
1+1+1+.... and since the remaining terms are non negative, or >0, then the sum must be >0