15£®Ä³Í¬Ñ§ÔÚÑо¿ÏàÁÚÈý¸öÕûÊýµÄËãÊõƽ·½¸ùÖ®¼äµÄ¹Øϵʱ£¬·¢ÏÖÒÔÏÂÈý¸öʽ×Ó¾ùÊÇÕýÈ·µÄ£º¢Ù$\sqrt{1}$+$\sqrt{3}$£¼2$\sqrt{2}$£»¢Ú$\sqrt{2}$+$\sqrt{4}$£¼2$\sqrt{3}$£»¢Û$\sqrt{3}$+$\sqrt{5}$£¼2$\sqrt{4}$
£¨1£©ÒÑÖª$\sqrt{2}¡Ê£¨1.41$£¬1.42£©£¬$\sqrt{3}¡Ê£¨1.73$£¬1.74£©£¬$\sqrt{5}¡Ê£¨2.23$£¬2.24£©£¬Çë´ÓÒÔÉÏÈý¸öʽ×ÓÖÐÈÎÑ¡Ò»¸ö£¬½áºÏ´Ë·¶Î§£¬ÑéÖ¤ÆäÕýÈ·ÐÔ£¨×¢Òâ²»ÄܽüËƼÆË㣩£»
£¨2£©Ç뽫´Ë¹æÂÉÍƹãÖÁÒ»°ãÇéÐΣ¬²¢Ö¤Ã÷Ö®£®

·ÖÎö £¨1£©½áºÏ´Ë·¶Î§£¬ÑéÖ¤ÆäÕýÈ·ÐÔ£¬
£¨2£©Ò»°ã½áÂÛΪ£ºÈôn¡ÊN*£¬Ôò$\sqrt{n}+\sqrt{n+2}£¼2\sqrt{n+1}$£¬Ó÷ÖÎö·¨ºÍ×ۺϷ¨¼´¿ÉÖ¤Ã÷£®

½â´ð ½â£º£¨1£©ÑéÖ¤¢Ùʽ³ÉÁ¢£º¡ß$\sqrt{3}£¼1.74$£¬
¡à$\sqrt{1}+\sqrt{3}£¼2.74$£¬
¡ß$\sqrt{2}£¾1.41$£¬
¡à$2\sqrt{2}£¾2.82$£¬
¡à$\sqrt{1}+\sqrt{3}£¼2\sqrt{2}$
£¨2£©Ò»°ã½áÂÛΪ£ºÈôn¡ÊN*£¬Ôò$\sqrt{n}+\sqrt{n+2}£¼2\sqrt{n+1}$£¬Ö¤Ã÷ÈçÏ£º
Ö¤·¨Ò»£ºÒªÖ¤£º$\sqrt{n}+\sqrt{n+2}£¼2\sqrt{n+1}$
Ö»ÐèÖ¤£º${£¨\sqrt{n}+\sqrt{n+2}£©^2}£¼{£¨2\sqrt{n+1}£©^2}$
¼´Ö¤£º$2n+2+2\sqrt{n}\sqrt{n+2}£¼4n+4$
Ò²¾ÍÊÇÖ¤£º$\sqrt{n}\sqrt{n+2}£¼n+1$
Ö»ÐèÖ¤£ºn£¨n+2£©£¼n2+2n+1
¼´Ö¤£º0£¼1£¬ÏÔÈ»³ÉÁ¢
¹Ê$\sqrt{n}+\sqrt{n+2}£¼2\sqrt{n+1}$£¬
Ö¤·¨¶þ£º$\sqrt{n+2}-\sqrt{n+1}$=$\frac{{£¨\sqrt{n+2}-\sqrt{n+1}£©£¨\sqrt{n+2}+\sqrt{n+1£©}}}{{\sqrt{n+2}+\sqrt{n+1}}}$£¬
=$\frac{1}{{\sqrt{n+2}+\sqrt{n+1}}}$$\sqrt{n+1}-\sqrt{n}$£¬
=$\frac{{£¨\sqrt{n+1}-\sqrt{n}£©£¨\sqrt{n+1}+\sqrt{n}£©}}{{\sqrt{n+1}+\sqrt{n}}}$£¬
=$\frac{1}{{\sqrt{n+1}+\sqrt{n}}}$£¬
¡ßn¡ÊN*£¬$\sqrt{n+2}+\sqrt{n+1}£¾$$\sqrt{n+1}+\sqrt{n}£¾0$£¬
¡à$\frac{1}{{\sqrt{n+2}+\sqrt{n+1}}}£¼$$\frac{1}{{\sqrt{n+1}+\sqrt{n}}}$£¬
¡à$\sqrt{n+2}-\sqrt{n+1}£¼$$\sqrt{n+1}-\sqrt{n}$£¬
¡à$\sqrt{n}+\sqrt{n+2}£¼2\sqrt{n+1}$

µãÆÀ ±¾Ì⿼²éÁË·ÖÎö·¨ºÍ×ۺϷ¨£¬¹Ø¼üÕÆÎÕÖ¤Ã÷¸ñʽ£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

5£®¡÷ABCÄÚÓÐÒ»µãP£¬ÇÒPΪ¡÷ABCÈýÌõÖÐÏߵĽ»µã£¬ÔòµãPΪ¡÷ABCµÄ£¨¡¡¡¡£©
A£®ÄÚÐÄB£®ÍâÐÄC£®ÖØÐÄD£®´¹ÐÄ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ÒÑ֪˫ÇúÏßCÒÔF1£¨-2£¬0£©¡¢F2£¨2£¬0£©Îª½¹µã£¬ÇÒ¹ýµãP£¨7£¬12£©£®
£¨1£©ÇóË«ÇúÏßCÓëÆä½¥½üÏߵķ½³Ì£»
£¨2£©ÈôбÂÊΪ1µÄÖ±ÏßlÓëË«ÇúÏßCÏཻÓÚA£¬BÁ½µã£¬ÇÒ$\overrightarrow{OA}¡Í\overrightarrow{OB}$£¨OΪ×ø±êÔ­µã£©£®ÇóÖ±ÏßlµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®Ä³Ð£¸ß¶þÄ꼶ÔÚÒ»´ÎÊýѧ²âÑéºó£¬Ëæ»ú³éÈ¡Á˲¿·ÖѧÉúµÄÊýѧ³É¼¨×é³ÉÒ»¸öÑù±¾£¬µÃµ½ÈçÏÂƵÂÊ·Ö²¼Ö±·½Í¼£º
£¨1£©ÇóÕⲿ·ÖѧÉú³É¼¨µÄÑù±¾Æ½¾ùÊý$\overline x$ºÍÑù±¾·½²îs2£¨Í¬Ò»×éÊý¾ÝÓøÃ×éµÄÖеãÖµ×÷Ϊ´ú±í£©
£¨2£©ÓÉƵÂÊ·Ö²¼Ö±·½Í¼¿ÉÒÔÈÏΪ£¬¸ÃУ¸ß¶þѧÉúÔÚÕâ´Î²âÑéÖеÄÊýѧ³É¼¨X·þ´ÓÕý̬·Ö²¼$N£¨\overline x£¬{s^2}£©$£®
¢ÙÀûÓÃÕý̬·Ö²¼£¬ÇóP£¨X¡Ý129£©£»
¢ÚÈô¸ÃУ¸ß¶þ¹²ÓÐ1000ÃûѧÉú£¬ÊÔÀûÓâٵĽá¹û¹À¼ÆÕâ´Î²âÑéÖУ¬Êýѧ³É¼¨ÔÚ129·ÖÒÔÉÏ£¨º¬129·Ö£©µÄѧÉúÈËÊý£®£¨½á¹ûÓÃÕûÊý±íʾ£©
¸½£º¢Ù$\sqrt{210}$¡Ö14.5¢ÚÈôX¡«N£¨¦Ì£¬¦Ò2£©£¬ÔòP£¨¦Ì-2¦Ò£¼X£¼¦Ì+2¦Ò£©=0.9544£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

10£®¼×¡¢ÒÒ¡¢±ûÈýÈËÖÐÖ»ÓÐÒ»ÈËÈ¥ÓÎÀÀ¹ý»Æº×Â¥£¬µ±ËûÃDZ»Îʵ½Ë­È¥¹ýʱ£¬¼×˵£º¡°±ûûÓÐÈ¥¡±£»ÒÒ˵£º¡°ÎÒÈ¥¹ý¡±£»±û˵£º¡°¼×˵µÄÊÇÕæ»°¡±£®ÊÂʵ֤Ã÷£ºÈýÈËÖУ¬Ö»ÓÐÒ»ÈË˵µÄÊǼٻ°£¬ÄÇôÓÎÀÀ¹ý»Æº×Â¥µÄÈËÊÇ£¨¡¡¡¡£©
A£®¼×B£®ÒÒC£®±ûD£®²»ÄÜÈ·¶¨

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®m£¬nÊÇÁ½Ìõ²»Í¬µÄÖ±Ïߣ¬¦Á£¬¦ÂÊÇÁ½¸ö²»Í¬µÄƽÃ棬ÏÂÁÐÃüÌâÊÇÕæÃüÌâµÄÊÇ£¨¡¡¡¡£©
A£®Èôm¡Î¦Á£¬m¡Î¦Â£¬Ôò¦Á¡Î¦ÂB£®Èôm¡Í¦Á£¬¦Á¡Í¦Â£¬Ôò m¡Î¦Â
C£®Èôm?¦Á£¬m¡Í¦Â£¬Ôò ¦Á¡Í¦ÂD£®Èôm?¦Á£¬¦Á¡Í¦Â£¬Ôò m¡Í¦Â

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

7£®Éèa=0.991.01£¬b=1.010.99£¬c=log1.010.99£¬Ôò£¨¡¡¡¡£©
A£®c£¼b£¼aB£®c£¼a£¼bC£®a£¼b£¼cD£®a£¼c£¼b

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

4£®Ä³Ô°ÁÖ¹«Ë¾×¼±¸ÂÌ»¯Ò»¿é°ë¾¶Îª200Ã×£¬Ô²ÐĽÇΪ$\frac{¦Ð}{4}$µÄÉÈÐοյأ¨ÈçͼµÄÉÈÐÎOPQÇøÓò£©£¬ÉÈÐεÄÄÚ½Ó¾ØÐÎABCDΪһˮ³Ø£¬ÆäÓàµÄµØ·½ÖÖ»¨£¬Èô¡ÏCOP=¦Á£¬¾ØÐÎABCDµÄÃæ»ýΪS£¨µ¥Î»£ºÆ½·½Ã×£©£®
£¨1£©ÊÔ½«S±íʾΪ¹ØÓÚ¦ÁµÄº¯Êý£¬Çó³ö¸Ãº¯ÊýµÄ±í´ïʽ£»
£¨2£©½Ç¦ÁÈ¡ºÎֵʱ£¬Ë®³ØµÄÃæ»ý S×î´ó£¬²¢Çó³öÕâ¸ö×î´óÃæ»ý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

5£®¶ÔÒ»¸öÈÝÆ÷ΪNµÄ×ÜÌå³éÈ¡ÈÝÁ¿ÎªnµÄÑù±¾£¬µ±Ñ¡Ôñ¼òµ¥Ëæ»ú³éÑù¡¢ÏµÍ³³éÑùºÍ·Ö²ã³éÑùÈýÖÖ²»Í¬·½·¨³éÈ¡Ñù±¾Ê±£¬×ÜÌåÖÐÿ¸ö¸öÌå±»³éÖеĸÅÂÊ·Ö±ðΪa¡¢b¡¢c£¬Ôò£¨¡¡¡¡£©
A£®a=b£¼cB£®b=c£¼aC£®a=c£¼bD£®a=b=c

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸