Question

若abc为正数,则(a+b+c)(1/a+1/b+1/c)的最小值

Answer 1

(a+b+c)(1/a+1/b+1/c)
=1+1+1+a/b+b/a+a/c+c/a+b/c+c/b
>=3+2√a/b*b/a+2√a/c*c/a+2√c/b*b/c
=3+2+2+2=9,当且仅当a=b=c时取“=”