已知集合A={x|1<ax<2},集合B={x||x|<1}.当A B时,求a的取值范围
已知集合A={x|1<ax<2},集合B={x||x|<1}.当AB时,求a的取值范围....
已知集合A={x|1<ax<2},集合B={x||x|<1}.当A B时,求a的取值范围.
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试题分析:根据B={x||x|<1},求得B={x|-1<x<1},由A?B,及A={x|1<ax<2},解含参数的不等式1<ax<2,对a 进行讨论,并求出此时乱塌满足题干的a应满足的条件,解不等式即可求得实数a的范围.. 试题解析:由已知,B={x|-1<x<1}. (ⅰ)当a=0时,A= ![](https://iknow-pic.cdn.bcebos.com/cefc1e178a82b901b1c9f381708da9773912ef18?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,显然A?B. (ⅱ)当a>0时, ![](https://iknow-pic.cdn.bcebos.com/0ff41bd5ad6eddc49eb484493adbb6fd52663334?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,要使A ![](https://iknow-pic.cdn.bcebos.com/f703738da9773912b341b5d3fb198618367ae218?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) B,必须 ![](https://iknow-pic.cdn.bcebos.com/4b90f603738da977c64bb699b351f8198618e318?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,所以a≥源旁2. (ⅲ)当a<0时, ![](https://iknow-pic.cdn.bcebos.com/dcc451da81cb39db649357e4d3160924ab183034?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,要使A ![](https://iknow-pic.cdn.bcebos.com/f703738da9773912b341b5d3fb198618367ae218?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) B,必须 ![](https://iknow-pic.cdn.bcebos.com/d1160924ab18972b0c693078e5cd7b899e510a34?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto) ,即a≤-2.综上可知,a≤-2或a=0或a≥2. |
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