??З????1,√2a?1???g′(x)<0??g(1) = 0????????g(x)<0????????????a??????(?∞,2]?2 2016ё?м2?(??)????9?(?21).??A???E:x24+y23= 1????????k(k >0)????E?A,M????N?E??MA⊥NA?(1)?|AM|=|AN|З??△AMN????(2)?2|AM|=|AN|З????√3< k <2???第(1)小题主要考查椭圆的对称性;第(2)小题考查椭圆的弦长计算,已知弦长的关系反向推算斜率k的范围为问题带来了新的变化.??????о??????OAMNxy(1)?|AM|=|AN|З?△MAN??????????????ц???Н?k= 1?A?????(?2,0)?????AM????x=y?2????E??????Н?y?712y?1?= 0,???M?????127???Н?△AMN???S=?127?2=14449.(2)?m=1k(m>0)????AM????x=my?2????E?????Н??m24+13?y2?my= 0,???M?????12m3m2+4????N??????12m3m2+4=?12m3 +4m2,???2|AM|=|AN|Н?2·√1 +m2·12m3m2+4=…1 +1m2·12m3 +4m2,2 2016ё?м2?(??)????10???8m3?3m2+6m?4 = 0.???f(x) = 8x3?3x2+6x?4(x >0)??????f′(x) = 24x2?6x+6>0,????f(x)????????f?1√3?=26?15√33√3=√676?√6753√3>0,?f?12?=?34<0,????f(x)?????????????12,1√3?????Н?12< m<1√3???√3< k <2?
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