增加两道自拟题目

题库0.3/Problems.json

@@ -512767,6 +512767,46 @@
         "space": "4em",
         "unrelated": []
     },
+    "019843": {
+        "id": "019843",
+        "content": "解下列关于$x$的不等式或方程:\\\\\n(1) $|2x-4|>5-x$;\\\\\n(2) $\\dfrac{x-a}{x-2}>1$;\\\\\n(3) $1+\\dfrac{a}{(x-2-a)(x-1)}=0$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20230927\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "019844": {
+        "id": "019844",
+        "content": "(1) 设$a,b,c$均为正数, 且$ab+bc+ca=1$, 求证: $a+b+c\\ge \\sqrt{3}$;\\\\\n(2) 设$a,b$均为非负实数, 求证: $a^3+b^3\\ge \\sqrt{ab}(a^2+b^2)$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20230927\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "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.",