13£®ÈçͼÐÎËÆ¡°w¡±µÄº¯ÊýÊÇÓÉÅ×ÎïÏßy1µÄÒ»²¿·Ö£¬Æä±í´ïʽΪ£ºy1=$\frac{\sqrt{3}}{3}$£¨x2-2x-3£©£¨x¡Ü3£©ÒÔ¼°Å×ÎïÏßy2µÄÒ»²¿·ÖËù¹¹³ÉµÄ£¬ÆäÖÐÇúÏßy2ÓëÇúÏßy1¹ØÓÚÖ±Ïßx=3¶Ô³Æ£¬A¡¢BÊÇÇúÏßy1ÓëxÖáÁ½½»µã£¨AÔÚBµÄ×ó±ß£©£¬CÊÇÇúÏßy1ÓëyÖá½»µã£®
£¨1£©ÇóA£¬B£¬CÈýµãµÄ×ø±êºÍÇúÏßy2µÄ±í´ïʽ£»
£¨2£©ÎÒÃÇ°ÑÆäÖÐÒ»Ìõ¶Ô½ÇÏß±»ÁíÒ»Ìõ¶Ô½ÇÏß´¹Ö±ÇÒÆ½·ÖµÄËıßÐγÆÎªóÝÐΣ®¹ýµãC×÷xÖáµÄƽÐÐÏßÓëÇúÏßy1½»ÓÚÁíÒ»¸öµãD£¬Á¬½ÓAD£®ÊÔÎÊ£ºÔÚÇúÏßy2ÉÏÊÇ·ñ´æÔÚÒ»µãM£¬Ê¹µÃËıßÐÎACDMΪóÝÐΣ¿Èô´æÔÚ£¬¼ÆËã³öµãMµÄºá×ø±ê£¬Èô²»´æÔÚ£¬ËµÃ÷ÀíÓÉ£®

·ÖÎö £¨1£©Çó³öµãC£¬y2ÓëxÖáµÄ½»µã×ø±ê£¬ÔÙÓÉ´ý¶¨ÏµÊý·¨Çó³öº¯Êýy2½âÎöʽ¼´¿É£»
£¨2£©ÏÈÈ·¶¨³öµãPµÄ×ø±êºÍCPµÄ½âÎöʽ£¬´Ó¶øÇó³öMµãµÄºá×ø±ê£®

½â´ð ½â£º£¨1£©ÔÚy1=$\frac{\sqrt{3}}{3}$£¨x2-2x-3£©ÖУ¬
Áîy1=0£¬ÔòÓÐ$\frac{\sqrt{3}}{3}$£¨x2-2x-3£©=0£¬
½âµÃx=-1»òx=3£¬
¡àA£¨-1£¬0£©£¬B£¨3£¬0£©£¬
¡ßCΪÇúÏßy1ÓëyÖáµÄ½»µã£¬
¡àC£¨0£¬-$\sqrt{3}$£©£®
ÓÖ¡ßÇúÏßy1ÓëÇúÏßy2¹ØÓÚÖ±Ïßx=3¶Ô³Æ£¬
¡àÇúÏßy2ÓëxÖáÁ½½»µã×ø±ê·Ö±ðΪ£¨3£¬0£©Ó루7£¬0£©£¬
¡ày2=$\frac{\sqrt{3}}{3}$£¨x-3£©£¨x-7£©=$\frac{\sqrt{3}}{3}$£¨x2-10x+21£©£¨£¨x¡Ý3£©
£¨2£©Èçͼ£¬

¹ýµãD×÷DG¡ÍxÖᣬ¹ýµãP×÷PH¡ÍxÖᣬ
¡àPH=$\frac{1}{2}$DG=$\frac{\sqrt{3}}{2}$£¬AH=$\frac{1}{2}$AG=$\frac{3}{2}$£¬
¡àOH=AH-AO=$\frac{1}{2}$£¬
¡àP£¨$\frac{1}{2}$£¬$\frac{\sqrt{3}}{2}$£©£¬
¡àÉèÏß¶ÎADµÄ´¹Ö±Æ½·ÖÏßCPµÄ½âÎöʽΪy=kx+m£¬
¡ßµãC£¨0£¬-$\sqrt{3}$£©£¬
¡à$\left\{\begin{array}{l}{\frac{k}{2}+m=\frac{\sqrt{3}}{2}}\\{m=-\sqrt{3}}\end{array}\right.$£¬
¡à$\left\{\begin{array}{l}{k=\sqrt{3}}\\{m=-\sqrt{3}}\end{array}\right.$£¬
¡àCPµÄ½âÎöʽΪy=$\sqrt{3}$x-$\sqrt{3}$£¬
¡ßy2=$\frac{\sqrt{3}}{3}$£¨x2-10x+21£©Óë¡àx=$\frac{13+\sqrt{73}}{2}$»òx=$\frac{13-\sqrt{73}}{2}$£¨Éᣬ¡ßx£¼3£©£®
¡àxM=$\frac{13+\sqrt{73}}{2}$£®

µãÆÀ ´ËÌâÊǶþ´Îº¯Êý×ÛºÏÌ⣬Ö÷Òª¿¼²éÁËÈ·¶¨º¯ÊýµÄ½»µã×ø±ê£¬ºÍ´ý¶¨ÏµÊý·¨È·¶¨º¯Êý½âÎöʽ£¬Çóº¯Êý½âÎöʽÊǽⱾÌåµÄ¹Ø¼ü£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®ÎÒ¹úµÚÒ»ËÒº½¿Õĸ½¢¡°ÁÉÄþºÅ¡°ÔÚº£ÉÏ·þÒÛ£¬½¢ÔØ»úÔÚ¿ÕÖзÉÐÐÖ´ÐÐÈÎÎñ£¬ÐèÒª½¢ÉϵĿÕÖмÓÓÍ»ú¸ø²¹³äÓÍ£¬Èçͼ¼×Ëùʾ£¬ÔÚ¿ÕÖмÓÓ͹ý³ÌÖУ¬Éè½¢ÔØ»úµÄÓÍÏäÖеÄÓàÓÍÁ¿Q1¶Ö£¬¼ÓÓÍ·É»úµÄ¼ÓÓÍÓÍÏäÖеÄÓàÓÍÁ¿ÎªQ2¶Ö£¬¼ÓÓÍʱ¼äΪt·ÖÖÓQ1¡¢Q2ÓëtÖ®¼äµÄº¯ÊýͼÏóÈçͼ¼×Ëùʾ£®Çë»Ø´ðÏÂÁÐÎÊÌ⣺
£¨1£©¼ÓÓÍ·É»úµÄ¼ÓÓÍÏäÖÐ×°ÔØÁË5.2¶ÖÓÍ£¬½«ÕâЩÓÍÈ«²¿¼Ó¸ø½¢ÔØ»úÐèÒª5·ÖÖÓ£»
£¨2£©Çó¼ÓÓ͹ý³ÌÖУ¬½¢ÔØ»úµÄÓÍÏäÖеÄÓàÓÍÁ¿Q1£¨¶Ö£©Óëʱ¼ät£¨·ÖÖÓ£©µÄº¯Êý¹ØÏµÊ½£¨²¢Ö±½Óд³ö×Ô±äÁ¿µÄȡֵ·¶Î§£©£»
£¨3£©Çó´Ó¼ÓÓÍ¿ªÊ¼¾­¹ý¼¸·ÖÖÓ¼ÓÓÍ»úµÄÓÍÏäÖеÄÓàÓÍÁ¿Óë½¢ÔØ»úÖеÄÓàÓÍÁ¿Ïàͬ£»
£¨4£©´Ó¼ÓÍêÓÍ¿ªÊ¼£¨´Ëʱ½¢ÔØ»úÔÚ¿ÕÖоຽ¿Õĸ½¢700ǧÃ×£©£¬º½¿Õĸ½¢ÒÔ200ǧÃ×/СʱÏò¶«º½ÐУ¬¶ø½¢ÔØ»úÔòÒÔ800ǧÃ×/СʱÏòÎ÷·ÉÐÐÖ´ÐÐÈÎÎñ£¬½¢ÔØ»ú¾àº½¿Õĸ½¢µÄ¾àÀëΪy£¬·ÉÐÐʱ¼äΪx£¬ÔòyÓëxÖ®¼äµÄº¯ÊýͼÏóÈçͼÒÒËùʾ£®ÔÚ²»ÄÜÔٴοÕÖмÓÓ͵ÄÇé¿öÏ£¬ÎªÁ˱£Ö¤½¢ÔØ»ú°²È«µÄ½µÂ亽¿Õĸ½¢ÉÏ£¬Ò»¶¨Ê±¼ä±ØÐë·µ»Ø£®ÇóaµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

4£®Èçͼ£¬BDΪһֱÏߣ¬¡ÏB=¡ÏC£¬AEƽ·Ö¡ÏDAC£¬Çë˵Ã÷AE¡ÎBC£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

1£®Èçͼ£¬ÔÚÆ½ÃæÖ±½Ç×ø±êϵÖУ¬µãA£¨0£¬n£©£¬B£¨m£¬0£©ÖеÄm£¬nÊÇ·½³Ì×é$\left\{\begin{array}{l}{m+n=-2}\\{m-n=-14}\end{array}\right.$µÄ½â£¬µãCÔÚxÖáµÄÕý°ëÖáÉÏ£¬ÇÒOA=2OC£¬AB=10£¬¹ýµãA×÷AD¡ÍyÖᣬ¹ýµãC×÷CD¡ÍADÓÚµãD£¬¶¯µãP´ÓµãD³ö·¢£¬ÒÔÿÃë2¸öµ¥Î»³¤¶ÈµÄËÙ¶ÈÔÚÉäÏßDAÉÏÔ˶¯£¬Í¬Ê±ÁíÒ»¶¯µãQ´ÓµãB³ö·¢ÏòÖÕµãAÔ˶¯£¬ËÙ¶ÈÊÇÿÃë3¸öµ¥Î»³¤¶È£¬Ò»µãÍ£Ö¹Ô˶¯ÁíÒ»µãҲֹͣ£¬ÉèÔ˶¯Ê±¼äΪtÃ룮
£¨1£©Çó³öµãA¡¢B¡¢CµÄ×ø±ê£»
£¨2£©Á¬½ÓPC£¬ÇëÓú¬tµÄ¹ØÏµÊ½À´±íʾ¡÷PACµÄÃæ»ýS£»
£¨3£©ÊÇ·ñ´æÔÚijһʱ¿Ìt£¬Ê¹¡÷PACµÄÃæ»ýµÈÓÚ¡÷BOQÃæ»ýµÄÒ»°ë£¿Èô´æÔÚÇëÇó³ötÖµ£¬Èô²»´æÔÚÇë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

8£®Èçͼ£¬ÔÚRt¡÷ABCÖУ¬¡ÏC=90¡ã£¬¡ÏBAC=40¡ã£¬ADÊÇ¡÷ABCµÄÒ»Ìõ½Çƽ·ÖÏߣ¬µãE£¬F£¬G·Ö±ðÔÚAD£¬AC£¬BCÉÏ£¬ÇÒËıßÐÎCGEFÊÇÕý·½ÐΣ¬Ôò¡ÏDEBµÄ¶ÈÊýΪ£¨¡¡¡¡£©
A£®40¡ãB£®45¡ãC£®50¡ãD£®55¡ã

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®Èçͼ£¬±ß³¤Îª8µÄÕý·½ÐÎOABCµÄÁ½±ßÔÚ×ø±êÖáÉÏ£¬ÒÔµãCΪ¶¥µãµÄÅ×ÎïÏß¾­¹ýµãA£¬µãPÊÇÅ×ÎïÏßÉϵãA¡¢C¼äµÄÒ»¸ö¶¯µã£¨º¬¶Ëµã£©£¬¹ýµãP×÷PD¡ÍOAÓÚµãD£¬µãE£¨8£¬2£©£¬F£¨0£¬6£©£¬Á¬½ÓPE¡¢PF¡¢EF£®
£¨1£©Ö±½Óд³öÅ×ÎïÏߺÍÖ±ÏßEFµÄ½âÎöʽ£®
£¨2£©Ð¡Ã÷̽¾¿µãPµÄλÖ÷¢ÏÖ£ºµ±µãPÓëµãA»òµãCÖØºÏʱ£¬PDÓëPFµÄºÍΪ¶¨Öµ£¬½ø¶ø²ÂÏ룺¶ÔÓÚÈÎÒâÒ»µãP£¬PDÓëPFµÄºÍΪ¶¨Öµ£¬ÇëÄãÅжϸòÂÏëÊÇ·ñÕýÈ·£¬²¢ËµÃ÷ÀíÓÉ£®
£¨3£©Ð¡Ã÷½øÒ»²½Ì½¾¿µÃ³ö½áÂÛ£º
¢ÙʹµÃPD-PE×î´óµÄµãPÊÇ·ñ´æÔÚ£¿Èô´æÔÚÇó³öµãPµÄ×ø±ê£¬·ñÔò˵Ã÷ÀíÓÉ£®
¢ÚÈô½«¡°Ê¹¡÷PEFµÃÃæ»ýΪÕûÊý¡±µÄµãP¼Ç×÷¡°ºÃµã¡±£¬ÇÒ´æÔÚ¶à¸ö¡°ºÃµã¡±£¬ÇëÖ±½Óд³öËùÓС°ºÃµã¡±µÄ¸öÊý£¬Çó³öʹµÃ¡÷PEFµÄÃæ»ý×î´óµÄºÃµãPµÄ×ø±ê£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

5£®Èçͼ£¬ÒÑÖª¡ÑAµÄ°ë¾¶Îª4£¬ECÊÇÔ²µÄÖ±¾¶£¬µãBÊÇ¡ÑAµÄÇÐÏßCBÉϵÄÒ»¸ö¶¯µã£¬Á¬½ÓAB½»¡ÑAÓÚµãD£¬ÏÒEFƽÐÐÓÚAB£¬Á¬½ÓDF£¬AF£®
£¨1£©ÇóÖ¤£º¡÷ABC¡Õ¡÷ABF£»
£¨2£©µ±¡ÏCAB=60¡ãʱ£¬ËıßÐÎADFEΪÁâÐΣ»
£¨3£©µ±AB=4$\sqrt{2}$ʱ£¬ËıßÐÎACBFΪÕý·½ÐΣ®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

2£®ÒÑÖªÒ»´Îº¯Êýy1=x+5µÄͼÏóÓë·´±ÈÀýº¯Êýy2=$\frac{k}{x}$µÄͼÏó½»ÓÚA¡¢BÁ½µã£¬ÒÑÖªµãAµÄºá×ø±êΪ1£®
£¨1£©Çó·´±ÈÀýº¯ÊýµÄ½âÎöʽ£»
£¨2£©ÇóµãBµÄ×ø±ê£¬²¢Ö±½Óд³öµ±y1£¼y2ʱxµÄȡֵ·¶Î§£»
£¨3£©µ±x£¾1ʱ£¬ÔÚ·´±ÈÀýͼÏóÉÏÓÐÒ»µãC£¬Ê¹µÃ¡÷ABCµÄÃæ»ýΪ21£¬ÇóµãCµÄ×ø±ê£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

8£®ÈçͼÌÝÐÎABCDÖУ¬AD¡ÎBC£¬FΪADµÄÖе㣬Á¬½ÓBF²¢ÑÓ³¤ÓëCDµÄÑÓ³¤Ïß½»ÓÚµãE£¬ÇÒ¡ÏABE=¡ÏACE£®
£¨1£©Ð´³öͼÖÐÈý¶ÔÏàËÆÈý½ÇÐΣ¨²»ÐèÒªÖ¤Ã÷£©£®
£¨2£©Ö¤Ã÷£º$\frac{EF}{BE}$=$\frac{FG}{BG}$£®
£¨3£©ÈôBG=2£¬EF=1£¬ÇóFGµÄ³¤£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸