作业帮求解：一道高二数学题要有详细解题过程
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求解：一道高二数学题要有详细解题过程
求解：一道高二数学题
要有详细解题过程
求解：一道高二数学题要有详细解题过程
x,y∈R+.xy-（x+y）＝1,则
A.x+y≥（2√2+1）.B.xy≤√2+1,C,x+y≤（√2+1）².D.xy≥2（√2+1）
设x+y＝a,xy＝b,则 x,y是方程 x²-ax+b＝0 的两个正根.b＝a+1
x²-ax+a+1＝0有两个正根.a²-4a-4≥0（注意a≥√（a²-4a-4）,此时两根正）
从a²-4a-4≥0,a＞0 得到a＝x+y≥2+2√2＝2（√2+1）＞2√2+1
xy＝b＝a+1≥2（√2+1）+1＞2（√2+1）.
∴ xy-（x+y）＝1时,A,D成立（A,D是必要条件,不是充分条件.）
对xy:
x+y>=2(xy)^(1/2)
1=xy-(x+y)<=xy-2(xy)^(1/2)
2<=xy-2(xy)^(1/2)+1=[(xy)^(1/2)-1]^2
2^(1/2)<=(xy)^(1/2)-1
(xy)^(1/2)>=1+2^(1/2)
xy>=[1+2^(1/2)]^2=3+2*2^(1/2)
没答案
对x+y...
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对xy:
x+y>=2(xy)^(1/2)
1=xy-(x+y)<=xy-2(xy)^(1/2)
2<=xy-2(xy)^(1/2)+1=[(xy)^(1/2)-1]^2
2^(1/2)<=(xy)^(1/2)-1
(xy)^(1/2)>=1+2^(1/2)
xy>=[1+2^(1/2)]^2=3+2*2^(1/2)
没答案
对x+y:
x+y>=2(xy)^(1/2)
(x+y)^2>=4xy
1=xy-(x+y)<=(1/4)(x+y)^2-(x+y)
2<=[(x+y)/2-1]^2
2^(1/2)<=(x+y)/2-1
x+y>=2(1+2^(1/2))
A比较像
收起
题目可能有问题
对xy:
x+y>=2(xy)^(1/2)
1=xy-(x+y)<=xy-2(xy)^(1/2)
2<=xy-2(xy)^(1/2)+1=[(xy)^(1/2)-1]^2
2^(1/2)<=(xy)^(1/2)-1
(xy)^(1/2)>=1+2^(1/2)
xy>=[1+2^(1/2)]^2=3+2*2^(1/2)
...
全部展开
题目可能有问题
对xy:
x+y>=2(xy)^(1/2)
1=xy-(x+y)<=xy-2(xy)^(1/2)
2<=xy-2(xy)^(1/2)+1=[(xy)^(1/2)-1]^2
2^(1/2)<=(xy)^(1/2)-1
(xy)^(1/2)>=1+2^(1/2)
xy>=[1+2^(1/2)]^2=3+2*2^(1/2)
没答案
对x+y:
x+y>=2(xy)^(1/2)
(x+y)^2>=4xy
1=xy-(x+y)<=(1/4)(x+y)^2-(x+y)
2<=[(x+y)/2-1]^2
2^(1/2)<=(x+y)/2-1
x+y>=2(1+2^(1/2))
看上去A比较像
收起