若负数a,b,c满足a+b+c=-1,则1/a+1/b+1/c的最大值为?

Question

若负数a,b,c满足a+b+c=-1,则1/a+1/b+1/c的最大值为?

Answer 1

(a+b+c)(1/a+1/b+1/c)=3+a/b+b/a+a/c+c/a+b/c+b/a,当a=b=c时,由均值定理,上式有最小值3+6倍根号2,又因为a,b,c为负数,所以原式有最大值-3-6倍根号2