ÌâÄ¿ÄÚÈÝ

1£®ÔĶÁÏÂÃæ×ÊÁÏ£º
$\frac{1}{1+\sqrt{2}}$=$\frac{1¡Á£¨\sqrt{2}-1£©}{£¨\sqrt{2}+1£©£¨\sqrt{2}-1£©}$=$\sqrt{2}$-1£» 
 $\frac{1}{\sqrt{3}+\sqrt{2}}$=$\frac{\sqrt{3}-\sqrt{2}}{£¨\sqrt{3}+\sqrt{2}£©£¨\sqrt{3}-\sqrt{2}£©}$=$\sqrt{3}$-$\sqrt{2}$£»        
$\frac{1}{\sqrt{5}+2}$=$\frac{\sqrt{5}-2}{£¨\sqrt{5}+2£©£¨\sqrt{5}-2£©}$=$\sqrt{5}$-2£®
ÊÔÇ󣺣¨1£©$\frac{1}{\sqrt{7}+\sqrt{6}}$µÄÖµ£»
£¨2£©$\frac{1}{3\sqrt{2}+\sqrt{17}}$µÄÖµ£»
£¨3£©£¨$\frac{1}{1+\sqrt{2}}$+$\frac{1}{\sqrt{2}+\sqrt{3}}$+¡­+$\frac{1}{\sqrt{2008}+\sqrt{2009}}$+$\frac{1}{\sqrt{2009}+\sqrt{2010}}$£©•£¨1+$\sqrt{2010}$£©£®

·ÖÎö £¨1£©Ô­Ê½·ÂÕÕÔĶÁ²ÄÁÏÖеķ½·¨Çó³öÖµ¼´¿É£»
£¨2£©Ô­Ê½·ÂÕÕÔĶÁ²ÄÁÏÖеķ½·¨Çó³öÖµ¼´¿É£»
£¨3£©Ô­Ê½µÚÒ»¸öÀ¨ºÅÖзÂÕÕÔĶÁ²ÄÁÏÖеķ½·¨±äÐΣ¬¼ÆËã¼´¿ÉµÃµ½½á¹û£®

½â´ð ½â£º£¨1£©Ô­Ê½=$\frac{\sqrt{7}-\sqrt{6}}{£¨\sqrt{7}+\sqrt{6}£©£¨\sqrt{7}-\sqrt{6}£©}$=$\sqrt{7}$-$\sqrt{6}$£»
£¨2£©Ô­Ê½=$\frac{3\sqrt{2}-\sqrt{17}}{£¨3\sqrt{2}+\sqrt{17}£©£¨3\sqrt{2}-\sqrt{17}£©}$=3$\sqrt{2}$-$\sqrt{17}$£»
£¨3£©Ô­Ê½=£¨$\sqrt{2}$-1+$\sqrt{3}$-$\sqrt{2}$+¡­+$\sqrt{2009}$-$\sqrt{2008}$+$\sqrt{2010}$-$\sqrt{2009}$£©•£¨1+$\sqrt{2010}$£©
=£¨$\sqrt{2010}$-1£©£¨$\sqrt{2010}$+1£©
=2010-1
=2009£®

µãÆÀ ´ËÌ⿼²éÁË·ÖĸÓÐÀí»¯£¬ÅªÇåÔĶÁ²ÄÁÏÖеķ½·¨ÊǽⱾÌâµÄ¹Ø¼ü£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com

¾«Ó¢¼Ò½ÌÍø