...ax^2+by^2=1与直线X+Y-1=0相交于AB两点,C是AB中点,若AB=2根号2...答:把y=1-x,①代入椭圆方程得ax^2+b(1-2x+x^2)=1,整理得(a+b)x^2-2bx+b-1=0,△=4b^2-4(a+b)(b-1)=4(a+b-ab),AB=√(2△)/|a+b|=2√2,平方,化简得a+b-ab=(a+b)^2,② 设A(x1,y1),B(x2,y2),则x1+x2=2b/(a+b),∴xC=(x1+x2)/2=b/(a+b),由...
...x恒成立,则a的取值范围,答案是(根号2/2,1),求高手解答过程答:当0<x≤1/2时,0<4^x<log x=lgx/lga,lgx<0,∴lga<0,∴0<a<1.这时4^x↑,logx↓,∴4^(1/2)<log(1/2),即2<log(1/2)=-lg2/lga,∴(2lga+lg2)/lga<0,∴-(1/2)lg2<lga<0,∴√2/2<a<1.