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°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

11£®ÔÚ¡÷ABCÖУ¬AB=13£¬BC=10£¬BC±ßÉϵÄÖÐÏßAD=12£¬ÔòAC=£¨¡¡¡¡£©
A£®10B£®11C£®12D£®13

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

12£®¶Ôij°à×éÖ¯µÄÒ»´Î¿¼ÊԳɼ¨½øÐÐͳ¼Æ£¬ÒÑÖª70.5¡«80.5·ÖÕâÒ»×éµÄƵÊýÊÇ12£¬ÆµÂÊÊÇ0.25£¬ÄÇô¸Ã°à¼¶µÄÈËÊýÊÇ48ÈË£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

9£®Ñ§Ð£ÎªÁË¿¼²ìÎÒУÆßÄ꼶ͬѧµÄÊÓÁ¦Çé¿ö£¬´ÓÆßÄ꼶µÄ10¸ö°à¹²540ÃûѧÉúÖУ¬Ã¿°à³éÈ¡ÁË8Ãû½øÐзÖÎö£¬ÔÚÕâ¸öÎÊÌâÖÐ×ÜÌåÊÇÆßÄ꼶540ÃûѧÉúµÄÊÓÁ¦Çé¿ö£¬Ñù±¾ÈÝÁ¿ÊÇ80£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®Èçͼ£¬½«Ò»¾ØÐÎֽƬABCDÕÛµþ£¬Ê¹Á½¸ö¶¥µãA£¬CÖغϣ¬ÕÛºÛΪFG..ÈôAB=8£¬BC=16£¬Ôò¡÷AEGµÄÃæ»ýΪ24£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ÒÑÖªaÊÇ·½³Ìx2-5x-1=0µÄÒ»¸ö¸ù£¬Ôò
£¨1£©a2-5a-1
£¨2£©a+$\frac{1}{a}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®Èçͼ£¬ADΪ¡÷ABCµÄÖÐÏߣ¬BEΪ¡÷ABDµÄÖÐÏߣ®
£¨1£©¡ÏABE=15¡ã£¬¡ÏBAD=40¡ã£¬Çó¡ÏBEDµÄ¶ÈÊý£»
£¨2£©×÷ͼ£ºÔÚ¡÷BEDÖÐ×÷BD±ßÉϵĸߣ¬´¹×ãΪF£»
£¨3£©Èô¡÷ABCµÄÃæ»ýΪ60£¬BD=6£¬Ôò¡÷BDEÖÐBD±ßÉϵĸßΪ¶àÉÙ£¿

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

10£®¼ÆË㣺
£¨1£©30+£¨-3£©2-£¨$\frac{1}{4}}$£©-1
£¨2£©a•a2•a3+£¨-2a3£©2-a8¡Âa2
£¨3£©£¨n-m£©3•£¨m-n£©2-£¨m-n£©5
£¨4£©314¡Á£¨-$\frac{1}{9}}$£©7£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®¼ÆË㣺-$\sqrt{18}$+|$\sqrt{2}$-2|-£¨$\frac{1}{2}$£©-1+2cos45¡ã£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸