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【OG20-P277-281题】
If x and y are positive numbers, is x+1y+1 >xy ?
(1)
(2)
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当前版本由
Helen 更新于2018-10-18 23:39:06 感谢由
Helen 对此题目的解答所做出的贡献。
(x+1)/(y+1)-x/y=(y-x)/[y(y+1)],要比较y和x的大小
条件1:y与x谁大谁小未知,不充分
条件2:y-x>0,(y-x)/[y(y+1)]>0,(x+1)/(y+1)>x/y,充分
题目讨论 (3条评论)

提交
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虫0515
化到(y-x)/y(y+1)>0,然后判断
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0 回复 2021-10-03 22:25:41
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孙大妮
题目相当于求(x+1)/(y+1)-x/y是否大于零,即(y-x)/y(y+1),x和y都是positive,只需分子x<y(2)即可证得,条件2充分
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0 回复 2018-11-25 14:26:48
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Adam贾
you can just suppose that the x is very very small,and the y is very very big,so y+1 will not influence the denominator;and because the x is very small,so we can not ignore it,it will change more than denominator,so the sfirst one is bigger than the second one.
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0 回复 2018-10-26 12:41:33