If a and b are positive, is (a-1 + b-1)-1 less than (a-1b-1)-1?
(1) a = 2b
(2) a + b > 1
首先根据已知有:
(a-1 + b-1)-1 =1/ (a-1 + b-1) =ab/(a+b)
(a-1b-1)-1=ab
如果 (a-1 + b-1)-1 less than (a-1b-1)-1则有 ab/(a+b) - ab < 0
条件一, a = 2b 代入 ab/(a+b) - ab < 0 则有 1/3*b < b^2 当b>1/3时1/3*b <b^2 成立;当0<b<1/3时1/3*b > b^2 答案不唯一;
条件二, a + b > 1代入ab/(a+b) - ab < 0 ,因为a,b均为正数,ab/(a+b) <ab 即1/(a+b)<1 a+b>1 正好符合条件 单独充分
所以选B |