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修改23499题面

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wangweiye7840 2024-01-29 15:43:40 +08:00
parent 3bbcefd79c
commit c0f109df39
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题库0.3/Problems.json
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@ -640147,7 +640147,7 @@
},
"023499": {
"id": "023499",
"content": "在等差数列 $\\{a_n\\}$ 中, 公差 $d \\neq 0$, $a_kx^2+2 a_{k+1}x+a_{k+2}=0$ ($k$ 为正整数).\\\\\n(1) 求证: 对不同的 $k$ 值, 方程都有公共根.\\\\\n(2) 若方程除公共根外的根依次为 $b_1, b_2, b_3, \\cdots, b_k, \\cdots$, 求证: 数列 $\\{\\dfrac{1}{b_k+1}\\}$ 是等差数列.\\\\\n(3) 设$\\{b_n\\}$是(2)中定义的数列. 若 $b_1=2$, 求 $b_{10}$.",
"content": "在各项均不为零的等差数列 $\\{a_n\\}$ 中, 公差 $d \\neq 0$. 考察如下的一组方程: $a_kx^2+2 a_{k+1}x+a_{k+2}=0$ ($k$ 为正整数).\\\\\n(1) 求证: 对不同的 $k$ 值, 方程都有公共根.\\\\\n(2) 若方程除公共根外的根依次为 $b_1, b_2, b_3, \\cdots, b_k, \\cdots$, 求证: 数列 $\\{\\dfrac{1}{b_k+1}\\}$ 是等差数列.\\\\\n(3) 设$\\{b_n\\}$是(2)中定义的数列. 若 $b_1=2$, 求 $b_{10}$.",
"objs": [],
"tags": [
"第四单元",
@ -640161,6 +640161,7 @@
"origin": "26届寒假作业补充题目",
"edit": [
"20240108\t王伟叶",
"20240129\t王伟叶",
"20240129\t王伟叶"
],
"same": [],