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添加自拟题目3题

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wangweiye7840 2023-07-26 15:01:47 +08:00
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题库0.3/Problems.json
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@ -494257,6 +494257,66 @@
"space": "4em",
"unrelated": []
},
"019299": {
"id": "019299",
"content": "设 $a, b, c \\in (0,+\\infty)$, 求证: $\\sqrt{a^2+b^2}+\\sqrt{b^2+c^2}+\\sqrt{c^2+a^2}\\geq \\sqrt{2}(a+b+c)$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20230726\t赵琍琍"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"019300": {
"id": "019300",
"content": "已知: $a, b, c \\in (0,+\\infty)$, 求证: $a^3+b^3+c^3 \\geq \\dfrac{1}{3}(a^2+b^2+c^2)(a+b+c)$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20230726\t赵琍琍"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"019301": {
"id": "019301",
"content": "已知: $a, b, c \\in (0,+\\infty)$, 求证: $a^4+b^4+c^4 \\geq a b c(a+b+c)$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20230726\t赵琍琍"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"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.",