Merge branch 'master' of ssh://wwylss.synology.me:30001/wangweiye/mathdeptv2

This commit is contained in:
weiye.wang 2023-09-18 18:29:19 +08:00
commit 68a6a59df5
2 changed files with 197 additions and 45 deletions

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@ -471,8 +471,7 @@
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@ -560,30 +547,27 @@
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View File

@ -142786,7 +142786,9 @@
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@ -270061,7 +270063,8 @@
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@ -510104,6 +510107,171 @@
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"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}.",
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"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{$x+\\dfrac{2}{y}\\le y+\\dfrac{1}{x}$}{$x+\\dfrac{1}{2y}\\le y+\\dfrac{1}{x}$}{$x-\\dfrac{2}{y}\\le y-\\dfrac{1}{x}$}{$x-\\dfrac{1}{2y}\\le y-\\dfrac{1}{x}$}",
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"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{$M<N<Q$}{$M<Q<N$}{$N<Q<M$}{$N<M<Q$}",
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"019834": {
"id": "019834",
"content": "解关于$x$的不等式: $mx+1>x+m^3$.",
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"origin": "新教材必修第一册习题-20230918修改",
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"019835": {
"id": "019835",
"content": "解下列不等式:\\\\\n(1) $6x^2-5x-1>0$;\\\\\n(2) $6x^2-5x-1<0$.",
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"content": "已知$a\\in \\mathbf{R}$, 求关于$x$的不等式 $x^2-(a+1)^2x+2a(a^2+1)<0$的解集.",
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"tags": [
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"019837": {
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"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.", "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.",
@ -514554,7 +514722,9 @@
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@ -514856,7 +515026,9 @@
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