6£®Ð¡Ã÷ÔÚ½â¾öÎÊÌ⣺ÒÑÖªa=$\frac{1}{{2+\sqrt{3}}}$£¬Çó2a2-8a+1µÄÖµ£®
ËûÊÇÕâÑù·ÖÎöÓë½âµÄ£º¡ßa=$\frac{1}{{2+\sqrt{3}}}$=$\frac{2-\sqrt{3}}{£¨2+\sqrt{3}£©£¨2-\sqrt{3}£©}$=2-$\sqrt{3}$
¡àa-2=$-\sqrt{3}$£¬¡à£¨a-2£©2=3£¬a2-4a+4=3
¡àa2-4a=-1£¬¡à2a2-8a+1=2£¨a2-4a£©+1=2¡Á£¨-1£©+1=-1£®
ÇëÄã¸ù¾ÝСÃ÷µÄ·ÖÎö¹ý³Ì£¬½â¾öÈçÏÂÎÊÌ⣺
£¨1£©»¯¼ò$\frac{1}{{\sqrt{3}+1}}+\frac{1}{{\sqrt{5}+\sqrt{3}}}+\frac{1}{{\sqrt{7}+\sqrt{5}}}+¡­+\frac{1}{{\sqrt{121}+\sqrt{119}}}$
£¨2£©Èôa=$\frac{1}{{\sqrt{2}-1}}$£¬¢ÙÇó4a2-8a+1µÄÖµ£»¢Úa3-3a2+a+1=0£®

·ÖÎö £¨1£©¸ù¾Ý·ÖĸÓÐÀí»¯µÄ·½·¨¿ÉÒÔ½â´ð±¾Ì⣻
£¨2£©¸ù¾ÝÌâÄ¿ÖеÄÀý×Ó¿ÉÒÔÁé»î±äÐνâ´ð±¾Ì⣮

½â´ð ½â£º£¨1£©$\frac{1}{{\sqrt{3}+1}}+\frac{1}{{\sqrt{5}+\sqrt{3}}}+\frac{1}{{\sqrt{7}+\sqrt{5}}}+¡­+\frac{1}{{\sqrt{121}+\sqrt{119}}}$
=$\frac{1}{2}$£¨$\sqrt{3}$-1£©+$\frac{1}{2}$£¨$\sqrt{5}$-$\sqrt{3}$£©+$\frac{1}{2}$£¨$\sqrt{7}$-$\sqrt{5}$£©+¡­+$\frac{1}{2}$£¨$\sqrt{121}$-$\sqrt{119}$£©£¬
=$\frac{1}{2}$£¨$\sqrt{121}$-1£©£¬
=$\frac{1}{2}$£¨11-1£©£¬
=5£®
£¨2£©¢Ù¡ßa=$\frac{1}{{\sqrt{2}-1}}$=$\frac{\sqrt{2}+1}{£¨\sqrt{2}-1£©£¨\sqrt{2}+1£©}$=$\sqrt{2}$+1£¬
¡àa-1=$\sqrt{2}$£¬
¡à£¨a-1£©2=2£¬¼´a2-2a=1£¬
¡à4a2-8a+1=4£¨a2-2a£©+1=4¡Á1+1=5£»
¢Ú¡ßa=$\frac{1}{{\sqrt{2}-1}}$=$\frac{\sqrt{2}+1}{£¨\sqrt{2}-1£©£¨\sqrt{2}+1£©}$=$\sqrt{2}$+1£¬
¡àa-1=$\sqrt{2}$£¬
¡à£¨a-1£©2=2£¬¼´a2-2a=1£¬
¡àa3-3a2+a+1
=a£¨a2-2a£©-a2+a+1
=a-a2+a+1
=-a2+2a+1
=-£¨a2-2a£©+1
=-1+1
=0£¬
¹Ê´ð°¸Îª£º0£®

µãÆÀ ±¾Ì⿼²é¶þ´Î¸ùʽµÄ»¯¼òÇóÖµ£¬½â´ð±¾ÌâµÄ¹Ø¼üÊÇÃ÷È·¶þ´Î¸ùʽ»¯¼òÇóÖµµÄ·½·¨£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®Èçͼ£¬ÒÑÖª¾ØÐÎABCDÖУ¬AB=1 cm£¬BC=2 cm£¬ÒÔBΪԲÐÄ£¬BCΪ°ë¾¶×÷$\frac{1}{4}$Ô²»¡½»ADÓÚµãF£¬½»BAµÄÑÓ³¤ÏßÓÚµãE£¬ÔòÉÈÐÎBCE±»¾ØÐÎËù½ØÊ£Óಿ·ÖµÄÃæ»ýΪ$\frac{2}{3}$¦Ð-$\frac{\sqrt{3}}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®¸ù¾ÝÄã·¢ÏֵĹæÂÉÌî¿Õ£º
¢ÙÒÑÖª$\root{3}{3}$=1.442£¬Ôò$\root{3}{0.003}$=0.1442£»
¢ÚÒÑÖª$\root{3}{0.000456}$=0.07696£¬Ôò$\root{3}{456}$=7.696£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

14£®ÏÂÃæÃüÌâÊÇÕæÃüÌâµÄÊÇ£¨¡¡¡¡£©
A£®ÓÐÁ½±ßºÍÒ»½Ç¶ÔÓ¦ÏàµÈµÄÁ½¸öÈý½ÇÐÎÈ«µÈ
B£®´¹Ö±ÓÚͬһÌõÖ±ÏßµÄÁ½Ö±ÏßƽÐÐ
C£®ÄÚ´í½ÇÏàµÈ
D£®ÓÐÒ»¸ö½ÇÊÇ60¡ãµÄµÈÑüÈý½ÇÐÎÊǵȱßÈý½ÇÐÎ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

1£®ÒÑÖª·½³Ì3x2m-n-4-5y3m+4n-1ÊǶþÔªÒ»´Î·½³Ì£¬Ôòm=2£¬n=-1£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®¹ØÓÚxµÄ·´±ÈÀýº¯Êý$y=\frac{1-m}{x}$£¨mΪ³£Êý£©£¬µ±x£¾0ʱ£¬yËæxµÄÔö´ó¶ø¼õС£¬ÔòmµÄÈ¡Öµ·¶Î§Îªm£¾1£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

18£®Ïà·´Êý¡¢Æ½·½¸ù¡¢Á¢·½¸ù¶¼µÈÓÚËü±¾ÉíµÄÊýÊÇ0£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®Èçͼ£¬BC¡ÍAB£¬CEƽ·Ö¡ÏBCD£¬DEƽ·Ö¡ÏADC£¬¡Ï2+¡Ï3=90¡ã£¬ÊÔÅжÏADÓëABµÄλÖùØϵ£¬²¢ËµÃ÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®ÔÚÏÂÁÐʵÊýÖУº0£¬$\root{3}{9}$£¬-3.1415£¬$\sqrt{4}$£¬$\frac{22}{7}$£¬0.343343334¡­£¨Ã¿Á½¸ö4Ö®¼ä3µÄ¸öÊýÖð½¥Ôö¼Ó1£©ÎÞÀíÊýÓУ¨¡¡¡¡£©
A£®1¸öB£®2¸öC£®3¸öD£®4¸ö

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸