Question

若a>0,b>0,c>0且a+b+c=1,则(1/a)+(1/b)+(1/c)有最小值( )

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

≥3+2+2+2

=9

B