Question

已知a,b,c.属于R+,且a+b+c=1,求证1/a+1/b+1/c>=9

Answer 1

1/a+1/b+1/c

=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c

=1+(b+c)/a+1(a+c)/b+1(a+b)/c

=3+b/c+c/b+a/c+c/a+a/b+b/a （由于b/a+a/b>=2,c/a+a/c>=2,c/b+b/c>=2）

>=3+2+2+2

=9