diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 50eb30d1..a4829fa1 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -272701,7 +272701,8 @@ "same": [], "related": [ "011853", - "030035" + "030035", + "019841" ], "remark": "", "space": "4em", @@ -512710,6 +512711,62 @@ "space": "4em", "unrelated": [] }, + "019841": { + "id": "019841", + "content": "用三角不等式证明: $|x+2|-|x-1|\\ge -3$, 对所有实数$x$均成立, 并求等号成立时$x$的取值范围.", + "objs": [ + "K0120001B", + "K0120002B" + ], + "tags": [ + "第一单元", + "2023届高三-第一轮复习讲义-03-等式与不等式的性质及证明" + ], + "genre": "4em", + "ans": "证明略, 等号成立时$x$的取值范围为$(-\\infty,-2]$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第一册习题-20230925修改", + "edit": [ + "20220806\t王伟叶", + "20230925\t王伟叶" + ], + "same": [], + "related": [ + "011853", + "030035", + "010104" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "019842": { + "id": "019842", + "content": "用三角不等式证明: $|x-3|-|x-5|\\le 2$对一切实数$x$恒成立, 并指出等号成立的条件.", + "objs": [], + "tags": [ + "第一单元" + ], + "genre": "4em", + "ans": "证明略, 等号成立当且仅当$x\\ge 5$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章-20230925修改", + "edit": [ + "20220901\t王伟叶\t伍杨超", + "20230925\t王伟叶" + ], + "same": [], + "related": [ + "020213" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.", @@ -518935,7 +518992,9 @@ "20220901\t王伟叶\t伍杨超" ], "same": [], - "related": [], + "related": [ + "019842" + ], "remark": "", "space": "4em", "unrelated": []