1/a+1/b+1/c=-(a+b+c)/a- (a+b+c)/b- (a+b+c)/c=-1-b/a-c/a-a/b-1-c/b-a/c-b/c-1
=-3-( b/a+ a/b+ c/a+ a/c+ c/b+ b/c)
因为a,b均为负数,所以b/a,a/b是正数.b/a+ a/b≥2.
同理：c/a+ a/c≥2 c/b+ b/c≥2
从而-3-( b/a+ a/b+ c/a+ a/c+ c/b+ b/c)≤-9
1/a+1/b+1/c的最大值是-9.