diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 438adcf7..b1e72e11 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/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 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 9da37e1b..1f864251 100644 --- a/题库0.3/Problems.json +++ b/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