diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 800b0cba..5f95802a 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -252610,7 +252610,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a=1$时, 解集为$\\varnothing$; 当$a>1$时, 解集为$(-\\infty,a+1)$; 当$a<1$时, 解集为$(a+1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -252634,7 +252634,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) $(-3,2)$; (2) $(-\\infty,-3)\\cup (2,+\\infty)$; (3) $(-\\infty,-3]\\cup [2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -252682,7 +252682,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$\\mathbf{R}$; (2) 解集为$\\varnothing$; (3) 解集为$(-\\infty,\\dfrac{1}{3})\\cup (\\dfrac{1}{3},+\\infty)$; (4) 解集为$\\varnothing$; (5) 解集为$\\mathbf{R}$; (6) 解集为$\\mathbf{R}$", "solution": "", "duration": -1, "usages": [], @@ -252706,7 +252706,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 如$x^2-6x+7<0$; (2) 如$x^2-6x+7>0$; (3) 如$x^2+1>0$; (4) 如$x^2+1<0$", "solution": "", "duration": -1, "usages": [], @@ -252731,7 +252731,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(3,+\\infty)$; (2) 解集为$[5,6)$.", "solution": "", "duration": -1, "usages": [], @@ -252755,7 +252755,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[\\dfrac{1}{4},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -252780,7 +252780,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\dfrac{1}{2},-\\dfrac{1}{3})$", "solution": "", "duration": -1, "usages": [], @@ -252805,7 +252805,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-\\infty,-1)\\cup (\\dfrac{3}{2},+\\infty)$; (2) 解集为$(-2,\\dfrac{1}{2}]$; (3) 解集为$(1,+\\infty)$; (4) 解集为$(-2,0]$; (5) 解集为$(2,3)$; (6) 解集为$\\varnothing$", "solution": "", "duration": -1, "usages": [], @@ -252830,7 +252830,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-7,1)$; (2) 解集为$(-\\infty,-1)\\cup (2,+\\infty)$; (3) 解集为$(1,+\\infty)$; (4) 解集为$(-\\infty,-2)\\cup (5,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -252854,7 +252854,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -252879,7 +252879,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 等号成立当且仅当$x=-1$", "solution": "", "duration": -1, "usages": [], @@ -252905,7 +252905,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "长与宽均为$\\dfrac{l}{4}$时", "solution": "", "duration": -1, "usages": [], @@ -252932,7 +252932,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "面积的最大值为$2$, 此时矩形的长与宽均为$\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -252956,7 +252956,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -267445,7 +267445,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -267551,7 +267551,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(x+1)(x^2-x+1)>(x-1)(x^2+x+1)$", "solution": "", "duration": -1, "usages": [], @@ -267599,7 +267599,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a=1$且$b=-1$时, $a^2+b^2=2a-2b-2$; 当$a\\ne 1$或$b\\ne -1$时, $a^2+b^2>2a-2b-2$.", "solution": "", "duration": -1, "usages": [], @@ -267623,7 +267623,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -267650,7 +267650,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -267674,7 +267674,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 等号成立当且仅当$a=b(>0)$", "solution": "", "duration": -1, "usages": [], @@ -267894,7 +267894,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -267918,7 +267918,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-\\infty,0)$; (2) 解集为$(2,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -267950,7 +267950,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-\\infty,a+2)$;\\\\\n(2) 解集为$(-\\infty,m^2+m+1)$;\\\\\n(3) 当$pq$时, 解集为$(-\\infty,p+q)$.", "solution": "", "duration": -1, "usages": [], @@ -267976,7 +267976,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-\\infty,2]\\cup [3,+\\infty)$; (2) 解集为$[-2,+\\infty)$; (3) 解集为$(-\\infty,1)\\cup (2,+\\infty)$; (4) 解集为$(-\\infty,-3)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -268003,7 +268003,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,1)\\cup [3,+\\infty)$; (2) $(-2,-1]$; (3) $(-\\infty,-2]\\cup (-1,+\\infty)$; (4) $(-\\infty,-2]\\cup (-1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -268075,7 +268075,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$\\{3\\}$; (2) 解集为$\\mathbf{R}$; (3) 解集为$\\varnothing$; (4) 解集为$\\mathbf{R}$", "solution": "", "duration": -1, "usages": [], @@ -268099,7 +268099,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$\\mathbf{R}$; (2) 解集为$\\mathbf{R}$; (3) 解集为$\\varnothing$; (4) 解集为$\\varnothing$", "solution": "", "duration": -1, "usages": [], @@ -268175,7 +268175,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-4,-3]$; (2) 解集为$(3-\\sqrt{5},\\dfrac{3}{4})$; (3) 解集为$(-\\infty,-1]\\cup (3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -268200,7 +268200,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-\\infty,-1)\\cup (2,+\\infty)$; (2) 解集为$(-\\infty,0)\\cup (1,+\\infty)$; (3) 解集为$[\\dfrac{1}{4},\\dfrac{3}{4})$; (4) 解集为$(-\\infty,-2)\\cup [\\dfrac{1}{2},+\\infty)$; (5) 解集为$(1,8)$", "solution": "", "duration": -1, "usages": [], @@ -268250,7 +268250,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(-1,\\dfrac{3}{2})$; (2) 解集为$(\\dfrac{4}{3},+\\infty)$; (3) 解集为$(-\\infty,\\dfrac{1}{2}]\\cup [3,+\\infty)$; (4) 解集为$(-1,4)$", "solution": "", "duration": -1, "usages": [], @@ -268275,7 +268275,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "约$46\\text{km/h}$($\\dfrac{67+\\sqrt{561}}{3}\\text{km/h}$)", "solution": "", "duration": -1, "usages": [], @@ -268299,7 +268299,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a=0$且$b<0$时, 解集为$\\mathbf{R}$; 当$a=0$且$b\\ge 0$时, 解集为$\\varnothing$; 当$a>0$时, 解集为$(\\dfrac{b}{a},+\\infty)$; 当$a<0$时, 解集为$(-\\infty,\\dfrac{b}{a})$", "solution": "", "duration": -1, "usages": [], @@ -268323,7 +268323,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 当$a=-3$时, 解集为$\\mathbf{R}$; 当$a>-3$时, 解集为$(-\\infty,-3]\\cup [a,+\\infty)$; 当$a<-3$时, 解集为$(-\\infty,a]\\cup [-3,+\\infty)$;\\\\\n(2) 当$a=0$时, 解集为$(-\\infty,0)\\cup (0,+\\infty)$; 当$a>0$时, 解集为$(-\\infty,a)\\cup (2a,+\\infty)$; 当$a<0$时, 解集为$(-\\infty,2a)\\cup (a,+\\infty)$\n(3) 解集为$(-\\infty,a]\\cup [a+1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -268372,7 +268372,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$[\\dfrac{4}{9},\\dfrac{1}{2})$; (2) 解集为$(-\\infty,-1)\\cup (0,1)$; (3) 解集为$[\\dfrac{5}{2},4)$", "solution": "", "duration": -1, "usages": [], @@ -268396,7 +268396,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$[-1,\\dfrac{1}{2}]$; (2) 解集为$[1,2)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -268421,7 +268421,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$[-3,0)\\cup (1,4]$; (2) 解集为$(-4,-1)\\cup (5,8)$; (3) 解集为$(-\\infty,\\dfrac{2}{3})\\cup (4,+\\infty)$; (4) 解集为$(-1,0)$", "solution": "", "duration": -1, "usages": [], @@ -268447,7 +268447,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(\\dfrac{3}{2},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -268474,7 +268474,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[0,8)$", "solution": "", "duration": -1, "usages": [], @@ -268498,7 +268498,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -268595,7 +268595,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -268621,7 +268621,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$25\\text{cm}^2$", "solution": "", "duration": -1, "usages": [], @@ -268695,7 +268695,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$2ab0$时, $(a+1)^2>a^2-a+1$; 当$a=0$时, $(a+1)^2=a^2-a+1$; 当$a<0$时, $(a+1)^20$时, 解集为$(-\\infty,\\dfrac{1}{a})$; 当$a=0$时, 解集为$\\mathbf{R}$; 当$a<0$时, 解集为$(\\dfrac{1}{a},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -312083,7 +312083,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a\\le 0$时, 解集为$\\varnothing$; 当$a>0$时, 解集为$(-\\dfrac{a}{2},2a)$.", "solution": "", "duration": -1, "usages": [], @@ -312107,7 +312107,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "解集为$(-1,3)$", "solution": "", "duration": -1, "usages": [], @@ -312157,7 +312157,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "解集为$[\\dfrac{3-\\sqrt{5}}{4},\\dfrac{3+\\sqrt{5}}{4}]$", "solution": "", "duration": -1, "usages": [], @@ -312179,7 +312179,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a=1$时, 解集为$(-\\infty,1)\\cup (1,+\\infty)$; 当$a=-1$时, 解集为$(-\\infty,-1)\\cup (-1,+\\infty)$; 当$a>1$或$-10$", "solution": "", "duration": -1, "usages": [], @@ -312267,7 +312267,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a>1$时, 解集为$[1,a]$; 当$a=1$时, 解集为$\\{1\\}$; 当$a<1$时, 解集为$[a,1]$", "solution": "", "duration": -1, "usages": [], @@ -312289,7 +312289,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$m<-2$时, 解集为$(-\\dfrac{2}{m},-1)$; 当$m=-2$时, 解集为$(-\\infty,-1)\\cup (-1,+\\infty)$; 当$-20$时, 解集为$(-\\infty,-1)\\cup (\\dfrac{2}{m},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -312311,7 +312311,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -312357,7 +312357,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-3,5)$", "solution": "", "duration": -1, "usages": [], @@ -312379,7 +312379,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(5,9)$", "solution": "", "duration": -1, "usages": [], @@ -312401,7 +312401,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$b=-3$, $c=2$, 解集为$(-\\infty,-2]\\cup [\\dfrac{1}{3},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -312423,7 +312423,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(5,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -312445,7 +312445,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,\\dfrac{1}{\\beta})\\cup (\\dfrac{1}{\\alpha},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -312467,7 +312467,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,-7)$; (2) $(-7,-3]$", "solution": "", "duration": -1, "usages": [], @@ -312489,7 +312489,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-3,4)$", "solution": "", "duration": -1, "usages": [], @@ -312511,7 +312511,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[-3,1)$", "solution": "", "duration": -1, "usages": [], @@ -312533,7 +312533,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-2]\\cup [1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -312555,7 +312555,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[3.1,100]$", "solution": "", "duration": -1, "usages": [], @@ -312577,7 +312577,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[-5,-3)\\cup (6,10]$", "solution": "", "duration": -1, "usages": [], @@ -312599,7 +312599,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a<-\\dfrac{1}{2}$或$a>1$时, $\\dfrac{a+2}{a-1}>-1$; 当$a=-\\dfrac{1}{2}$时, $\\dfrac{a+2}{a-1}=-1$; 当$-\\dfrac{1}{2}-\\dfrac{1}{4}$时, 解集为$(-\\infty,\\dfrac{-1-\\sqrt{1+4a}}{2}]\\cup [\\dfrac{-1+\\sqrt{1+4a}}{2},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -494026,7 +494026,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[-1,2]$; (2) 不存在", "solution": "", "duration": -1, "usages": [], @@ -494049,7 +494049,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,2)$; (2) $(6,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -494072,7 +494072,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$(\\dfrac{-1+\\sqrt{7}}{2},\\dfrac{1+\\sqrt{3}}{2})$", "solution": "", "duration": -1, "usages": [], @@ -494095,7 +494095,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "当$a=0$时, 解集为$(-\\infty,0)\\cup (0,+\\infty)$; 当$a>0$时, 解集为$(-\\infty,-a)\\cup (0,+\\infty)$; 当$a<0$时, 解集为$(-\\infty,0)\\cup (-a,+\\infty)$;\\\\", "solution": "", "duration": -1, "usages": [], @@ -494118,7 +494118,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$(1,3)$", "solution": "", "duration": -1, "usages": [], @@ -494141,7 +494141,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$[-\\dfrac{1}{2},1)\\cup (1,\\dfrac{4}{3}]$", "solution": "", "duration": -1, "usages": [], @@ -494164,7 +494164,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "当$a<0$时, 解集为$(\\dfrac{a-2}{a-1},2)$; 当$a=1$, 解集为$\\varnothing$; 当$01$时, 解集为$(-\\infty,\\dfrac{a-2}{a-1})\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -494187,7 +494187,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$a=4$, $b=2$", "solution": "", "duration": -1, "usages": [], @@ -494210,7 +494210,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-7)\\cup (\\dfrac{4}{3},+\\infty)$; $(-\\infty,\\dfrac{1}{2}]\\cup (3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -494233,7 +494233,7 @@ "不等式" ], "genre": "4em", - "ans": "", + "ans": "(1) $(-\\sqrt{5},-1)\\cup (1,\\sqrt{5})$; (2) $(\\dfrac{3}{2},2)\\cup (2,\\dfrac{5}{2})$; (3) $\\{1,2\\}$", "solution": "", "duration": -1, "usages": [], @@ -494259,7 +494259,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,\\dfrac{2}{5}]\\cup (\\dfrac{1}{2},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -494282,7 +494282,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "当$a=1$时, 解集为$\\varnothing$; 当$a>1$时, 解集为$(\\dfrac{a+1}{2},+\\infty)$; 当$a<1$时, 解集为$(-\\infty,\\dfrac{a+1}{2})$", "solution": "", "duration": -1, "usages": [], @@ -494305,7 +494305,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "$(1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -494328,7 +494328,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -494351,7 +494351,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -494374,7 +494374,7 @@ "不等式" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -508456,7 +508456,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -508522,7 +508522,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $x(x-y)>y(x-y)$;\\\\\n(2) $(3a+1)(a+1)<2(a+1)^2-3$.", "solution": "", "duration": -1, "usages": [ @@ -508549,7 +508549,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 1{bc}-\\dfrac 1{ac}<\\dfrac 1{abc}$", "solution": "", "duration": -1, "usages": [ @@ -508576,7 +508576,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{a^2}b+\\dfrac{b^2}a>a+b$", "solution": "", "duration": -1, "usages": [ @@ -508664,7 +508664,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -508739,7 +508739,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -508895,7 +508895,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a=b$时, $\\sqrt {ma+nb}=m\\sqrt a+n\\sqrt b$; 当$a\\ne b$时, $\\sqrt {ma+nb}>m\\sqrt a+n\\sqrt b$.", "solution": "", "duration": -1, "usages": [ @@ -509005,7 +509005,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,\\dfrac{5}{6})$", "solution": "", "duration": -1, "usages": [ @@ -509063,7 +509063,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a>-\\dfrac{6}{11}$时, 解集为$(-\\infty,\\dfrac{5a+6}{3})$; 当$a\\le -\\dfrac{6}{11}$时, 解集为$\\varnothing$", "solution": "", "duration": -1, "usages": [ @@ -509094,7 +509094,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "当$a=b$时, 解集为$\\varnothing$; 当$a>b$时, 解集为$(\\dfrac{a+b}{a-b},+\\infty)$; 当$a0$时, 解集为$(-2a,\\dfrac{1}{a})$; 当$a<0$时, 解集为$(-2a,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -509182,7 +509182,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-\\dfrac{1}{2},0]$", "solution": "", "duration": -1, "usages": [ @@ -509238,7 +509238,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 解集为$(1,a)$; (2) 解集为$(a,2a)$", "solution": "", "duration": -1, "usages": [ @@ -509266,7 +509266,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-4,1]\\cup [3,4)$; (2) $\\mathbf{R}$; (3) $(-\\infty,-4]\\cup (1,3)\\cup [4,+\\infty)$; (4) $\\varnothing$", "solution": "", "duration": -1, "usages": [ @@ -509296,7 +509296,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 当$a=1$时, 解集为$\\varnothing$; 当$a\\ne 1$时, 解集为$(2a,a^2+1)$;\\\\\n(2) 当$a<2$时, 解集为$(-\\infty,-2)\\cup (-a,+\\infty)$; 当$a\\ge 2$时, 解集为$(-\\infty,-a)\\cup (-2,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -509349,7 +509349,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(-3,0]$", "solution": "", "duration": -1, "usages": [], @@ -509373,7 +509373,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[0,1)$", "solution": "", "duration": -1, "usages": [], @@ -509395,7 +509395,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[0,1)$", "solution": "", "duration": -1, "usages": [], @@ -509417,7 +509417,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[1,19)$", "solution": "", "duration": -1, "usages": [], @@ -509441,7 +509441,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=4$, $b=3$", "solution": "", "duration": -1, "usages": [], @@ -509491,7 +509491,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[-\\dfrac{1}{2},1]$", "solution": "", "duration": -1, "usages": [], @@ -509513,7 +509513,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[\\dfrac{3}{2},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -509538,7 +509538,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "\\begin{tabular}{c|cc}\n& $A\\cap B$ & $A\\cup B$ \\\\ \\hline\n$a>0$ & $(a,3a)$ & $(-a,+\\infty)$ \\\\\n$a=0$ & $\\varnothing$ & $(0,+\\infty)$ \\\\\n$a<0$ & $(a,-a)$ & $(3a,+\\infty)$\n\\end{tabular}", "solution": "", "duration": -1, "usages": [], @@ -509560,7 +509560,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=-1$", "solution": "", "duration": -1, "usages": [], @@ -509582,7 +509582,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=1$", "solution": "", "duration": -1, "usages": [], @@ -509604,7 +509604,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\mathbf{R}$", "solution": "", "duration": -1, "usages": [], @@ -509626,7 +509626,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,0)\\cup (1,+\\infty)$; (2) $(1,8)$; (3) $(-\\infty,0)\\cup (3,+\\infty)$; (4) $(-\\infty,-2]\\cup [1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -509692,7 +509692,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1)\\cup (-1,1)$", "solution": "", "duration": -1, "usages": [], @@ -509714,7 +509714,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-b)\\cup (-a,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -509738,7 +509738,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -509760,7 +509760,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 当$a\\ge 0$时, 解集为$(-\\infty,1)\\cup (a+1,+\\infty)$; 当$a<0$时, 解集为$(-\\infty,a+1)\\cup (1,+\\infty)$;\\\\\n(2) 当$a\\le 0$时, 解集为$(-\\infty,\\dfrac{1}{1-a})\\cup (1,+\\infty)$; 当$01$时, 解集为$(\\dfrac{1}{1-a},1)$.", "solution": "", "duration": -1, "usages": [], @@ -509806,7 +509806,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -509828,7 +509828,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-3]\\cup [5,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -509850,7 +509850,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,-\\dfrac{1}{2})$; (2) $(1,\\sqrt{2})$; (3) $[-5,5]$; (4) $(-\\infty,-3)\\cup (4,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -509872,7 +509872,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=-1$, $b=2$", "solution": "", "duration": -1, "usages": [], @@ -509896,7 +509896,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -509920,7 +509920,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -509947,7 +509947,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -509971,7 +509971,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$(0,-2+\\sqrt{5}]$", "solution": "", "duration": -1, "usages": [], @@ -510037,7 +510037,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -510061,7 +510061,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2,3)$", "solution": "", "duration": -1, "usages": [], @@ -510083,7 +510083,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$a=\\dfrac{1}{4}$, $b=-1$", "solution": "", "duration": -1, "usages": [], @@ -510105,7 +510105,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\infty,\\dfrac{1}{2}]\\cup [5,+\\infty)$; (2) $\\{0\\}\\cup [1,\\dfrac{5}{2}]$", "solution": "", "duration": -1, "usages": [], @@ -510127,7 +510127,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$[-3,2)$", "solution": "", "duration": -1, "usages": [], @@ -510149,7 +510149,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -510197,7 +510197,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$a\\ge 2$且$b\\ge 1$; $a-2=b-1\\ge 0$", "solution": "", "duration": -1, "usages": [], @@ -510219,7 +510219,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -510241,7 +510241,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(1) 小, $4$; (2) 大, $-4$", "solution": "", "duration": -1, "usages": [], @@ -510263,7 +510263,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "假", "solution": "", "duration": -1, "usages": [], @@ -510285,7 +510285,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{2}$, $-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -510307,7 +510307,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\ge$", "solution": "", "duration": -1, "usages": [], @@ -510329,7 +510329,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -510351,7 +510351,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -510375,7 +510375,7 @@ "第一单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -510397,7 +510397,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "不正确, 在基本不等式两边同除$ab$时没有考虑到$ab$的符号.", "solution": "", "duration": -1, "usages": [], @@ -510421,7 +510421,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$, $6$, $4$, $4$", "solution": "", "duration": -1, "usages": [], @@ -510443,7 +510443,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$; $-1$", "solution": "", "duration": -1, "usages": [], @@ -510465,7 +510465,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -510487,7 +510487,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "小, $8$", "solution": "", "duration": -1, "usages": [], @@ -510509,7 +510509,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{4}$", "solution": "", "duration": -1, "usages": [], @@ -510533,7 +510533,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{2}}{2}$, $\\dfrac{1}{4}$", "solution": "", "duration": -1, "usages": [], @@ -510556,7 +510556,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [], @@ -510578,7 +510578,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -510622,7 +510622,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "大, $-2\\sqrt{2}$, $1-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -510644,7 +510644,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "大, $\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [], @@ -510691,7 +510691,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$x=\\sqrt{2}-1$, $y=2-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -510713,7 +510713,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -510737,7 +510737,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $8$; (2) $\\dfrac{9}{4}$; (3) $\\dfrac{5}{14}+\\dfrac{\\sqrt{6}}{7}$", "solution": "", "duration": -1, "usages": [], @@ -510759,7 +510759,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{1}{6}$", "solution": "", "duration": -1, "usages": [], @@ -510805,7 +510805,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略, 等号成立当且仅当$x\\ge 5$", "solution": "", "duration": -1, "usages": [], @@ -510827,7 +510827,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -510849,7 +510849,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,2]$", "solution": "", "duration": -1, "usages": [], @@ -510871,7 +510871,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -510893,7 +510893,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$13$或$-13$", "solution": "", "duration": -1, "usages": [], @@ -510915,7 +510915,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "(最大的区间为)$[\\dfrac{1}{8},\\dfrac{1}{7}]$", "solution": "", "duration": -1, "usages": [], @@ -510938,7 +510938,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -510960,7 +510960,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -511032,7 +511032,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "证明略", "solution": "", "duration": -1, "usages": [], @@ -511100,7 +511100,7 @@ "第一单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 证明略", "solution": "", "duration": -1, "usages": [],