10£®ÒÑÖªÊýÁÐ{an}µÄ¸÷ÏîΪÕýÊý£¬ÆäǰnÏîºÍΪSnÂú×ã${S_n}={£¨\frac{{{a_n}+1}}{2}£©^2}$£¬Éèbn=10-an£¨n¡ÊN£©£®
£¨1£©ÇóÖ¤£ºÊýÁÐ{an}ÊǵȲîÊýÁУ¬²¢Çó{an}µÄͨÏʽ£»
£¨2£©ÉèÊýÁÐ{bn}µÄǰnÏîºÍΪTn£¬ÇóTnµÄ×î´óÖµ£®
£¨3£©ÉèÊýÁÐ{bn}µÄͨÏʽΪ${b_n}=\frac{a_n}{{{a_n}+t}}$£¬ÎÊ£ºÊÇ·ñ´æÔÚÕýÕûÊýt£¬Ê¹µÃb1£¬b2£¬bm£¨m¡Ý3£¬m¡ÊN£©³ÉµÈ²îÊýÁУ¿Èô´æÔÚ£¬Çó³ötºÍmµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

·ÖÎö £¨1£©µ±n=1ʱ£¬${a_1}={S_1}={£¨\frac{{{a_1}+1}}{2}£©^2}$£¬½âµÃa1=1£®µ±n¡Ý2ʱ£¬an=Sn-Sn-1£¬»¯Îª£¨an+an-1£©£¨an-an-1-2£©=0£¬ÓÉÒÑÖª¿ÉµÃ£ºan-an-1-2=0£¬ÀûÓõȲîÊýÁеÄͨÏʽ¼´¿ÉµÃ³ö£®
£¨2£©bn=10-an=-2n+11£¬¿ÉµÃ{bn}ÊǵȲîÊýÁУ¬ÀûÓÃÇóºÍ¹«Ê½¡¢¶þ´Îº¯ÊýµÄµ¥µ÷ÐÔ¼´¿ÉµÃ³ö£®
£¨3£©ÓÉ£¨1£©Öª${b_n}=\frac{2n-1}{2n-1+t}$£®ÒªÊ¹b1£¬b2£¬bm³ÉµÈ²îÊýÁУ¬¿ÉµÃ2b2=b1+bm£¬´úÈ뻯¼ò¼´¿ÉµÃ³ö£®

½â´ð ½â£º£¨1£©µ±n=1ʱ£¬${a_1}={S_1}={£¨\frac{{{a_1}+1}}{2}£©^2}$£¬¡àa1=1¡­£¨2·Ö£©
µ±n¡Ý2ʱ£¬an=Sn-Sn-1=$£¨\frac{{a}_{n}+1}{2}£©^{2}$-$£¨\frac{{a}_{n-1}+1}{2}£©^{2}$£¬¼´£¨an+an-1£©£¨an-an-1-2£©=0£¬
¡ßÊýÁÐ{an}µÄ¸÷ÏîΪÕýÊý£¬¡àan+an-1£¾0£¬an-an-1-2=0£¬
ËùÒÔ{an}ÊǵȲîÊýÁУ¬¹«²îΪ2£®
¡àan=1+2£¨n-1£©=2n-1£®
£¨2£©bn=10-an=-2n+11£¬b1=9£¬
¡ßbn-bn-1=-2£¬¡à{bn}ÊǵȲîÊýÁС­£¨7·Ö£©
¡à${T_n}=\frac{{n£¨{b_1}+{b_n}£©}}{2}=-{n^2}+10n$£¬µ±n=5ʱ£¬${T_{nmax}}=-{5^2}+10¡Á5=25$¡­£¨10·Ö£©
£¨3£©ÓÉ£¨1£©Öª${b_n}=\frac{2n-1}{2n-1+t}$£®ÒªÊ¹b1£¬b2£¬bm³ÉµÈ²îÊýÁУ¬
¡à2b2=b1+bm£¬¼´$2¡Á\frac{3}{3+t}=\frac{1}{1+t}+\frac{2m-1}{2m-1+t}$£¬¡­£®ÕûÀíµÃ$m=3+\frac{4}{t-1}$£¬¡­1£¨2·Ö£©
ÒòΪm£¬tΪÕýÕûÊý£¬ËùÒÔtÖ»ÄÜÈ¡2£¬3£¬5£®
µ±t=2ʱ£¬m=7£»µ±t=3ʱ£¬m=5£»µ±t=5ʱ£¬m=4£®
¹Ê´æÔÚÕýÕûÊýt£¬Ê¹µÃb1£¬b2£¬bm³ÉµÈ²îÊýÁУ®¡­£¨16·Ö£©

µãÆÀ ±¾Ì⿼²éÁËÊýÁеÝÍÆ¹ØÏµ¡¢µÈ²îÊýÁеÄͨÏʽÓëÇóºÍ¹«Ê½¡¢¶þ´Îº¯ÊýµÄµ¥µ÷ÐÔ£¬·½³ÌµÄ½â·¨£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

19£®ÒÑÖªÍÖÔ²C£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1£¨a£¾b£¾0£©$¾­¹ýµã$£¨1£¬\frac{{2\sqrt{3}}}{3}£©$£¬×óÓÒ½¹µã·Ö±ðΪF1¡¢F2£¬Ô²x2+y2=2ÓëÖ±Ïßx+y+b=0ÏཻËùµÃÏÒ³¤Îª2£®
£¨¢ñ£©ÇóÍÖÔ²CµÄ±ê×¼·½³Ì£»
£¨¢ò£©ÉèQÊÇÍÖÔ²CÉϲ»ÔÚxÖáÉϵÄÒ»¸ö¶¯µã£¬QÎª×ø±êÔ­µã£¬¹ýµãF2×÷OQµÄƽÐÐÏß½»ÍÖÔ²CÓÚM¡¢NÁ½¸ö²»Í¬µÄµã
£¨1£©ÊÔ̽¾¿$\frac{|MN|}{{|OQ{|^2}}}$µÄÖµÊÇ·ñΪһ¸ö³£Êý£¿ÈôÊÇ£¬Çó³öÕâ¸ö³£Êý£»Èô²»ÊÇ£¬Çë˵Ã÷ÀíÓÉ£®
£¨2£©¼Ç¡÷QF2MµÄÃæ»ýΪS1£¬¡÷OF2NµÄÃæ»ýΪS2£¬ÁîS=S1+S2£¬ÇóSµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®Èçͼ£¬Ô²Ì¨µÄ¸ßΪ4£¬ÉÏ¡¢Ïµ×Ãæ°ë¾¶·Ö±ðΪ3¡¢5£¬M¡¢N·Ö±ðÔÚÉÏ¡¢Ïµ×ÃæÔ²ÖÜÉÏ£¬ÇÒ£¼$\overrightarrow{{O}_{2}M}$£¬$\overrightarrow{{O}_{1}N}$£¾=120¡ã£¬Ôò|$\overrightarrow{MN}$|µÈÓÚ£¨¡¡¡¡£©
A£®$\sqrt{65}$B£®5$\sqrt{2}$C£®$\sqrt{35}$D£®5

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®ÒÑÖª²»µÈʽ|x|+|x-3|£¼x+6µÄ½â¼¯Îª£¨m£¬n£©£®
£¨1£©Çóm£¬nµÄÖµ£»
£¨2£©Èôx£¾0£¬y£¾0£¬nx+y+m=0£¬ÇóÖ¤£ºx+y¡Ý16xy£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

5£®ÒÑÖªËÄÀâ×¶S-ABCDµÄµ×ÃæÎªÆ½ÐÐËıßÐΣ¬ÇÒSD¡ÍÆ½ÃæABCD£¬AB=2AD=2SD£¬¡ÏDCB=60¡ã£¬M£¬N·Ö±ðΪSB£¬SCµÄÖе㣬¹ýMN×÷Æ½ÃæMNPQ·Ö±ðÓëÏß¶ÎCD£¬ABÏཻÓÚµãP£¬Q£¬ÇÒ$\overrightarrow{AQ}=¦Ë\overrightarrow{AB}$£®
£¨1£©µ±$¦Ë=\frac{1}{2}$ʱ£¬Ö¤Ã÷£ºÆ½ÃæMNPQ¡ÎÆ½ÃæSAD£»
£¨2£©ÊÇ·ñ´æÔÚʵÊý¦Ë£¬Ê¹µÃ¶þÃæ½ÇM-PQ-BΪ60¡ã£¿Èô´æÔÚ£¬Çó³ö¦ËµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®ÉèÊýÁÐ{an}µÄǰnÏîºÍΪSn£¬ÒÑÖªa1=1£¬Sn+1=3Sn+2£¬n¡ÊN£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Èôbn=$\frac{8n}{{a}_{n+1}-{a}_{n}}$£¬ÇóÊýÁÐ{bn}µÄǰnÏîºÍTn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

2£®ÒÑÖª½Ç¦ÁµÄÖÕ±ßÔÚÖ±Ïß$y=-\sqrt{3}x$ÉÏ£¬
£¨1£©Çótan¦Á£¬²¢Ð´³öÓë¦ÁÖÕ±ßÏàͬµÄ½ÇµÄ¼¯ºÏS£»
£¨2£©ÇóÖµ$\frac{{\sqrt{3}sin£¨{¦Á-¦Ð}£©+5cos£¨{2¦Ð-¦Á}£©}}{{-\sqrt{3}cos£¨{\frac{3¦Ð}{2}+¦Á}£©+cos£¨{¦Ð+¦Á}£©}}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

19£®ÒÑÖªµãA£¨0£¬-2£©£¬ÍÖÔ²$E£º\frac{x^2}{a^2}+\frac{y^2}{b^2}=1£¨a£¾b£¾0£©$µÄÀëÐÄÂÊΪ$\frac{{\sqrt{2}}}{2}£¬F$£¬ÊÇÍÖÔ²EµÄÓÒ½¹µã£¬Ö±ÏßAFµÄбÂÊΪ2£¬OÎª×ø±êÔ­µã£®
£¨1£©ÇóEµÄ·½³Ì£»
£¨2£©Éè¹ýµãA¶¯Ö±ÏßlÓëEÏཻÓÚP£¬QÁ½µã£¬µ±OP¡ÍOQʱ£¬ÇólµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®ÒÑÖªÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{1}{2}$£¬ÉèA£¨0£¬b£©£¬B£¨a£¬0£©£¬F1£¬F2£¬·Ö±ðÊÇÍÖÔ²µÄ×óÓÒ½¹µã£¬ÇÒS${\;}_{¡÷AB{F}_{2}}$=$\frac{\sqrt{3}}{2}$
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©¹ýF1µÄÖ±ÏßÓëÒÔF2Ϊ½¹µã£¬¶¥µãÔÚ×ø±êÔ­µãµÄÅ×ÎïÏß½»ÓÚP£¬QÁ½µã£¬Éè$\overrightarrow{{F}_{1}P}$=¦Ë$\overrightarrow{{F}_{1}Q}$£¬Èô¦Ë¡Ê[2£¬3]£¬Çó¡÷F2PQÃæ»ýµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸