Question

已知a,b,c属于R+,a+b+c=1,求证（1/a-1）(1/b-1)(1/c-1)>=8

Answer 1

1/a－1＝(a+b+c)/a－1＝b/a＋c/a

1/b－1＝(a+b+c)/b－1＝a/b＋c/b

1/c－1＝(a+b+c)/c－1＝a/c＋b/c

（1/a-1）(1/b-1)(1/c-1)≥2√(b/a*c/a)×2√(a/b*c/b)×2√(a/c*b/c)＝8