收录高三寒假作业33新题

工具v2/文本文件/新题收录列表.txt

@@ -97,3 +97,6 @@
 20240125-114602
 023873:023882
 
+20240125-115018
+023883:023888
+

题库0.3/Problems.json

@@ -68083,7 +68083,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023888"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -110884,7 +110886,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023883"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -256408,7 +256412,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023885"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -381303,7 +381309,9 @@
             "20230123\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023883"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -447416,7 +447424,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023883"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -447614,7 +447624,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023884"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -644226,6 +644238,136 @@
         "space": "4em",
         "unrelated": []
     },
+    "023883": {
+        "id": "023883",
+        "content": "若方程 $x^2+p x+q=0$($p, q \\in \\mathbf{R}$) 有一个根为 $1+\\mathrm{i}$, 则 $p q=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "003544",
+            "013651",
+            "016260"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023884": {
+        "id": "023884",
+        "content": "在复数范围内因式分解:\\\\\n(1) $2 x^2-4 x+5=$\\blank{50}.\\\\\n(2) $x^4-16=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "016269"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023885": {
+        "id": "023885",
+        "content": "若复数 $z$ 满足 $|z|-z-5 \\mathrm{i}-1=0$, 则 $z=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "009091"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023886": {
+        "id": "023886",
+        "content": "设 $a \\in \\mathbf{R}$, 若关于 $x$ 的方程 $2 x^2-8 x+a+1=0$ 的一个虚根的模是 $\\sqrt{5}$, 则 $a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023887": {
+        "id": "023887",
+        "content": "设 $a \\in \\mathbf{R}, x_1, x_2$ 是关于 $x$ 的实系数一元二次方程 $x^2+3 a x+a^2+1=0$ 的两个不同虚根, 求 $\\dfrac{1}{x_1}+\\dfrac{1}{x_2}$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023888": {
+        "id": "023888",
+        "content": "已知关于 $x$ 的方程 $x^2+x+p=0$ 的两个复数根 $\\alpha, \\beta$ 满足 $|\\alpha-\\beta|=4$, 求实数 $p$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "002086"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",