添加三道自拟题目（2026届高一小测用)

题库0.3/Problems.json

@@ -510104,6 +510104,66 @@
         "space": "4em",
         "unrelated": []
     },
+    "019831": {
+        "id": "019831",
+        "content": "已知$\\alpha,\\beta$是方程$2x^2-\\sqrt{15}x+1=0$的两根, 则$|\\alpha-\\beta|$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20230918\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019832": {
+        "id": "019832",
+        "content": "已知$x,y$是正实数, 则下列条件中, ``$x\\le y$''的必要条件为\\bracket{20}.\n\\fourch{$x+\\dfrac{2}{y}\\le y+\\dfrac{1}{x}$}{$x+\\dfrac{1}{2y}\\le y+\\dfrac{1}{x}$}{$x-\\dfrac{2}{y}\\le y-\\dfrac{1}{x}$}{$x-\\dfrac{1}{2y}\\le y-\\dfrac{1}{x}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20230918\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "019833": {
+        "id": "019833",
+        "content": "已知三角形的三边长分别为$a,b,c$. 设$M=\\dfrac{a}{1+a}+\\dfrac{b}{1+b}$, $N=\\dfrac{c}{1+c}$, $Q=\\dfrac{a+b}{1+a+b}$, 则$M,N,Q$的大小关系为\\bracket{20}.\n\\fourch{$M<N<Q$}{$M<Q<N$}{$N<Q<M$}{$N<M<Q$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20230918\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "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.",