2012年空念数学杂志第一卷第9期2012年北约自主招生数学试题参考解答

2012c11ò19Ï77–80

Ò¤á …= x=y=z=31, ¤¦ .2479

8.¦¦ sin4xsin2x sinxsin3x=a3[0,π)k ) a.

1π)‰. f(x)=sin4xsin2x sinxsin3x=(cos4x cos6x)w,'ux=22πé¡,Ïdf(x)=a3[0,π)k ) {,7, U3x=0, .2 x=0 ) ,d a=0, §z sinxsin5x=03[0,π)Ø ),

π ) ,d a=1, §z sinxsin5x=1.Ï 3[0,π)þ2πsinx 0,¤± U´sinx=1,sin5x=1,=x= ).2nþ¤ã,a=1. x=9.¦y:e S Ê>/ z Ñ ,K§ Ê>/.

y². ù Ê>/ ABCDE,- AE,CD u:G,ë(AC.Ï ∠AED=∠EDC,¤±∠GED=∠GDE.qÏ A,C,D,Eo: ,¤±∠GAC=∠EDG=∠GED,¤±DE²1uCD,l DE=CD.ÓnkAE=BC,BC=DE,DE=AB,u´AB=BC=CD=DE=DA,=Ê>/ABCDE Ê>/. .5P. þã ÑyôÚòz¯K,ز Ï,ã' {ü,¢5Ø ã .

10.¦y:é?¿ ên,(1+s∈N+.

y². Eê an=(1+√n √n7 L«¤√√+ /ª,Ù¥√n+(1 ,K_^A { 2

an+2=2an+1+an,a1=1,a2=3, n∈N+,

u´{an} ê ., ,5¿

√2n√2n 2(1++(1 a2 1= 12n2

√2n 2√2n(1+ (1 =,2