设X>0,Y>0且X≠Y,比较X&u2l1 sup2 du1;/Y&u2l1 sup2 du1;+Y&u2l1 sup2 du1;/X&u2l1 sup2 du1;与X/y+y/x的大小

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"$5z1fi" '已知圆C:X^2+y^2-2x-2y+1=0,直线l:y=kx,且直线l与圆C相交于P、Q两个不同点。有一点M(0,b),满足MP⊥MQ。
当b∈(1,2/3)时,求k的取值范围。
把y=kx代入x^2+y^2-2x-2y+1=0,整理得
(1+k^2)x^2-(2+k)x+1=0,
设P(x1,y1),Q(x2,y2),则
x1+x2=(2+k)/(1+k^2),x1x2=1/(1+k^2).
向量MP=(x1,y1-b),MQ=(x2,y2-b),
由MP⊥MQ得
0=x1x2+(y1-b)(y2-b)
=x1x2+(kx1-b)(kx2-b)
=(1+k^2)x1x2-bk(x1+x2)+b^2
=1-bk(2+k)/(1+k^2)+b^2,
∴(1-b+b^2)k^2-2bk+1+b^2=0,
△=4b^2-4(1-b+b^2)(1+b^2)
=-4(1-b+b^2-b^3+b^4)<0(b∈(2/3,1)),
∴k的取值范围是空集。
其他答案(共1个回答)
f(1)=a+2b+c奇数,f(0)=c奇数,
所以a+2b是偶数,
所以a是偶数。
反设,如果存在整数零点k,
则ak^2+2bk+c=0
因为ak^2,2b...
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已知抛物线y^2=2px(p&0),准线l与x轴交与N点过焦点F作直线与抛物线交与A(x1,y1) B(x2,y2)使AB⊥AN,M1.证明:4x1x2=p&sup2;2.|x1-x2|的值(用p表示)3.求证:∠MAB=∠MBAM是点B在x轴上的射影.
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1.设过焦点F作直线斜率为k,过焦点F作直线方程:y=k(x-p/2),联立y^2=2px,消去y得:x^2-(p+2p/k^2)x+p^2/4=0x1,x2是此方程的两个根,x1x2=p^2/44x1x2=p&sup2;2..|x1-x2|=根号[(x1+x2)^2-4x1x2]=根号[(p+2p/k^2)^2-p^2]=2p/k^2*根号(k^2+1)3.需要补充
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