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B. C. D.,´ð°¸ C ÓÉÕâÁÐÊýµÄÌØµã¿ÉÖª,µÚn(n1,ÇÒnΪÕýÕûÊý)¸öÊýµÄ·ÖĸÊǵÚ(n-1)¸öÊý·ÖĸµÄ2±¶ ¼Ó1,·Ö×ÓΪn2,ËùÒÔµÚ5¸öÊýΪ = ,µÚ6¸öÊýΪ = = .¹ÊÑ¡C.,7.(2018ËÄ´¨³É¶¼,23,4·Ö)ÒÑÖªa0,S1= ,S2=-S1-1,S3= ,S4=-S3-1,S5= ,¡¡ ¼´µ±nΪ´óÓÚ1µÄ ÆæÊýʱ,Sn= ;µ±nΪ´óÓÚ1µÄżÊýʱ,Sn=-Sn-1-1 ,°´´Ë¹æÂÉ,S2 018= .(Óú¬aµÄ´úÊýʽ±í ʾ),´ð°¸ -,½âÎö S1= ,S2=- -1=- ,S3=- ,S4=- ,S5=-(a+1),S6=a,S7= ,¡¡,¡àS2 018=S2=- .,˼··ÖÎö ¸ù¾ÝÊýSnµÄ±ä»¯¹æÂÉ,·¢ÏÖSnµÄֵÿ6¸öһѻ·,ÒòΪ2 018=336¡Á6+2,ËùÒÔS2 018ÓëS2µÄ ÖµÏàͬ,´ËÌâµÃ½â.,·½·¨¹æÂÉ ±¾ÌâÊǹæÂÉ̽¾¿ÐÍÌâÖеÄÊý×ֵı仯ÀàÌâÄ¿.½â´ð¹æÂÉ̽¾¿ÐÍÌâÄ¿,Ò»°ãÊǶÔÓÐÏÞ µÄǰ¼¸¸öÊýÖµ¼ÆËã,¸ù¾ÝÕ⼸¸öÊýÖµµÄ±ä»¯¹æÂÉÕÒ³öËùÓÐÊýÖµµÄ±ä»¯¹æÂÉ,È·¶¨Ñ»·»òÓú¬n µÄ´úÊýʽ±íʾ¹æÂÉ,ÔÙ¸ù¾ÝÌâĿҪÇóÇó½â.,8.(2016ɽ¶«¶«Óª,18,4·Ö)ÔÚÇó1+3+32+33+34+35+36+37+38µÄֵʱ,Õź췢ÏÖ:´ÓµÚ¶þ¸ö¼ÓÊýÆðÿһ ¸ö¼ÓÊý¶¼ÊÇǰһ¸ö¼ÓÊýµÄ3±¶,ÓÚÊÇËý¼ÙÉè: S=1+3+32+33+34+35+36+37+38, ¢Ù È»ºóÔÚ¢ÙʽµÄÁ½±ß¶¼³Ë3, µÃ3S=3+32+33+34+35+36+37+38+39, ¢Ú ¢Ú-¢ÙµÃ3S-S=39-1,¼´2S=39-1, ËùÒÔS= . µÃ³ö´ð°¸ºó,°®¶¯ÄÔ½îµÄÕźìÏë:Èç¹û°Ñ¡°3¡±»»³É×Öĸm(m¡Ù0ÇÒm¡Ù1),ÄÜ·ñÇó³ö1+m+m2+m3+ m4+¡+m2 016µÄÖµ?Èç¹ûÄÜÇó³ö,ÆäÕýÈ·´ð°¸ÊÇ .,´ð°¸,½âÎö ÉèT=1+m+m2+m3+m4+¡+m2 016, ÔòmT=m+m2+m3+m4+¡+m2 016+m2 017, Á½Ê½Ïà¼õµÃ(m-1)T=m2 017-1,¡àT= .,9.(2018ºÓ±±,22,9·Ö)Èçͼ,½×ÌÝͼµÄÿ¸ǫ̈½×É϶¼±ê×ÅÒ»¸öÊý,´Óϵ½ÉϵĵÚ1¸öÖÁµÚ4¸ǫ̈½× ÉÏÒÀ´Î±ê×Å-5,-2,1,9,ÇÒÈÎÒâÏàÁÚËĸǫ̈½×ÉÏÊýµÄºÍ¶¼ÏàµÈ. ³¢ÊÔ (1)Çóǰ4¸ǫ̈½×ÉÏÊýµÄºÍÊǶàÉÙ. (2)ÇóµÚ5¸ǫ̈½×ÉϵÄÊýxÊǶàÉÙ. Ó¦Óà Çó´Óϵ½ÉÏǰ31¸ǫ̈½×ÉÏÊýµÄºÍ. ·¢ÏÖ ÊÔÓú¬k(kΪÕýÕûÊý)µÄʽ×Ó±íʾ³öÊý¡°1¡±ËùÔÚµĄ̈½×Êý.,½âÎö ³¢ÊÔ (1)-5-2+1+9=3. (2)ÓÉÌâÒâ,µÃ-5-2+1+9=-2+1+9+x, ½âµÃx=-5. Ó¦Óà Óë(2)ͬÀí,µÃµÚ6¸öµ½µÚ8¸ǫ̈½×ÉϵÄÊýÒÀ´ÎÊÇ-2,1,9,¿É¼ų̂½×ÉϵÄÊý´Óϵ½Éϰ´-5,-2, 1,9ËĸöÊýÒÀ´ÎÑ»·ÅÅÁÐ. ¡ß31=7¡Á4+3, ¡àǰ31¸ǫ̈½×ÉÏÊýµÄºÍΪ7¡Á3+(-5-2+1)=15. ·¢ÏÖ 4k-1.,˼··ÖÎö ³¢ÊÔ:(1)Ö±½ÓÁÐʽ,¼ÆËãËãʽµÄÖµ¼´¿É;(2)¸ù¾ÝÈÎÒâÏàÁÚËĸǫ̈½×ÉÏÊýµÄºÍÏàµÈÁÐ ³ö·½³Ì,µÃ½â.Ó¦ÓÃ:ͬ(2)µÄ·½·¨Çó³öµÚ6,7,8¸ǫ̈½×ÉϵÄÊý,·¢ÏÖ¹æÂÉΪ̨½×ÉϵÄÊý´Óϵ½ÉÏÿ Ëĸöһѻ·,½ø¶øÇó³ö´Óϵ½ÉÏǰ31¸ǫ̈½×ÉÏÊýµÄºÍ.·¢ÏÖ:¸ù¾Ý̨½×ÉϵÄÊýÿËĸöһѻ·,¿É ÖªÊý¡°1¡±ËùÔÚµĄ̈½×Êý¼ä¸ôΪ4,¼´¿ÉÇó½â.,·½·¨Ö¸µ¼ ¶ÔÓÚÊý×Ö(»òͼÐÎ)Ñ»·±ä»»Àà¹æÂÉÌâ,Çó¾¹ýN´Î±ä»»ºó¶ÔÓ¦µÄÊý×Ö(»òͼÐÎ)µÄ½â Ìâ²½Öè:1.ͨ¹ý¹Û²ìÕâ×éÊý×Ö(»òͼÐÎ),µÃµ½¸Ã×éÊý×Ö(»òͼÐÎ)¾¹ýÒ»¸öÑ»·±ä»»ÐèÒªµÄ´ÎÊý, ¼ÇΪn;2.ÓÃN³ýÒÔn,µ±ÄÜÕû³ýʱ,µÚN´Î±ä»»ºó¶ÔÓ¦µÄÊý×Ö(»òͼÐÎ)¾ÍÊÇÒ»¸öÑ»·±ä»»ÖÐ×îºóÒ» ´Î±ä»»ºó¶ÔÓ¦µÄÊý×Ö(»òͼÐÎ);µ±ÉÌbÓàm(0mn)ʱ,µÚN´Î±ä»»ºó¶ÔÓ¦µÄÊý×Ö(»òͼÐÎ)¾ÍÊÇÒ» ¸öÑ»·±ä»»ÖеÚm´Î±ä»»ºó¶ÔÓ¦µÄÊý×Ö(»òͼÐÎ).,10.(2017ºÓ±±,22,9·Ö)·¢ÏÖ ÈÎÒâÎå¸öÁ¬ÐøÕûÊýµÄƽ·½ºÍÊÇ5µÄ±¶Êý. ÑéÖ¤ (1)(-1)2+02+12+22+32µÄ½á¹ûÊÇ5µÄ¼¸±¶? (2)ÉèÎå¸öÁ¬ÐøÕûÊýµÄÖмäÒ»¸öΪn,д³öËüÃÇµÄÆ½·½ºÍ,²¢ËµÃ÷ÊÇ5µÄ±¶Êý. ÑÓÉì ÈÎÒâÈý¸öÁ¬ÐøÕûÊýµÄƽ·½ºÍ±»3³ýµÄÓàÊýÊǼ¸ÄØ?Çëд³öÀíÓÉ.,½âÎö ÑéÖ¤ (1)¡ß(-1)2+02+12+22+32=1+0+1+4+9=15=5¡Á3,¡à½á¹ûÊÇ5µÄ3±¶. (3·Ö) (2)ƽ·½ºÍΪ(n-2)2+(n-1)2+n2+(n+1)2+(n+2)2. (5·Ö) »¯¼òµÃ5n2+10=5(n2+2). ¡ßnΪÕûÊý,¡àÕâ¸öºÍÊÇ5µÄ±¶Êý. (7·Ö) ÑÓÉì ÓàÊýÊÇ2. (8·Ö) ÀíÓÉ:ÉèÖмäµÄÕûÊýΪn,(n-1)2+n2+(n+1)2=3n2+2±»3³ýÓà2. (9·Ö),˼··ÖÎö (1)ÏȼÆËãËãʽµÄÖµ,ÔÙÈ·¶¨±¶Êý;(2)ÏÈÓôúÊýʽ±íʾ³öÎå¸öÁ¬ÐøÕûÊýµÄƽ·½ºÍ,»¯ ¼òºóµÃ³ö½áÂÛ;(3)ÓôúÊýʽ±íʾ³öÈý¸öÁ¬ÐøÕûÊýµÄƽ·½ºÍ,»¯¼òºó±»3³ýµÃµ½ÓàÊý.,¿¼µã¶þ Çó´úÊýʽµÄÖµ,1.(2018¹óÖݹóÑô,1,3·Ö)µ±x=-1ʱ,´úÊýʽ3x+1µÄÖµÊÇ ( ) A.-1 B.-2 C.-3 D.-4,´ð°¸ B ½«x=-1´úÈë3x+1µÃ,3¡Á(-1)+1=-3+1=-2,¹ÊÑ¡B.,2.(2017±±¾©,7,3·Ö)Èç¹ûa2+2a-1=0,ÄÇô´úÊýʽ ¡¤ µÄÖµÊÇ ( ) A.-3 B.-1 C.1 D.3,´ð°¸ C ¡¤ = ¡¤ = ¡¤ =a2+2a,ÓÉa2+2a-1=0µÃa2+2a=1,¹ÊÔʽ= 1.¹ÊÑ¡C.,3.(2017ËÄ´¨ÃàÑô,12,3·Ö)ÈçͼËùʾ,½«ÐÎ×´¡¢´óСÍêÈ«ÏàͬµÄ¡°?¡±ºÍÏ߶ΰ´ÕÕÒ»¶¨¹æÂÉ°Ú³É ÏÂÁÐͼÐÎ.µÚ1·ùͼÖС°?¡±µÄ¸öÊýΪa1,µÚ2·ùͼÖС°?¡±µÄ¸öÊýΪa2,µÚ3·ùͼÖС°?¡±µÄ¸öÊý Ϊa3,¡¡,ÒÔ´ËÀàÍÆ,Ôò + + +¡+ µÄֵΪ ( ) A. B. C. D.,´ð°¸ C µÚ1·ùͼÖÐÓÐ3=1¡Á3¸ö¡°?¡±; µÚ2·ùͼÖÐÓÐ8=2¡Á4¸ö¡°?¡±; µÚ3·ùͼÖÐÓÐ15=3¡Á5¸ö¡°?¡±; ¡¡ µÚ19·ùͼÖÐÓÐ399=19¡Á21¸ö¡°?¡±. ËùÒÔ + + +¡+ = + + +¡+ = ¡Á = ¡Á = ,¹ÊÑ¡C.,4.(2016ÖØÇì,6,4·Ö)Èôa=2,b=-1,Ôòa+2b+3µÄֵΪ ( ) A.-1 B.3 C.6 D.5,´ð°¸ B µ±a=2,b=-1ʱ,Ôʽ=2+2¡Á(-1)+3=3,¹ÊÑ¡B.,5.(2015ɽ¶«Íþº£,12,3·Ö)Èçͼ,ÕýÁù±ßÐÎA1B1C1D1E1F1µÄ±ß³¤Îª2,ÕýÁù±ßÐÎA2B2C2D2E2F2µÄÍâ½Ó Ô²ÓëÕýÁù±ßÐÎA1B1C1D1E1F1µÄ¸÷±ßÏàÇÐ,ÕýÁù±ßÐÎA3B3C3D3E3F3µÄÍâ½ÓÔ²ÓëÕýÁù±ßÐÎA2B2C2D2E2 F2µÄ¸÷±ßÏàÇÐ,¡¡°´ÕâÑùµÄ¹æÂɽøÐÐÏÂÈ¥,ÕýÁù±ßÐÎA10B10C10D10E10F10µÄ±ß³¤Îª ( ) A. B. C. D.,´ð°¸ D ¡ßÕýÁù±ßÐÎA1B1C1D1E1F1µÄ±ß³¤Îª2= ,¡àÕýÁù±ßÐÎA2B2C2D2E2F2µÄÍâ½ÓÔ²µÄ°ë ¾¶Îª2¡Á = ,ÔòÕýÁù±ßÐÎA2B2C2D2E2F2µÄ±ß³¤Îª = ,ͬÀí,ÕýÁù±ßÐÎA3B3C3D3E3F3µÄ±ß ³¤Îª = ,¡¡,ÕýÁù±ßÐÎAnBnCnDnEnFnµÄ±ß³¤Îª ,Ôòµ±n=10ʱ,ÕýÁù±ßÐÎA10B10C10D10E 10F10µÄ±ß³¤Îª = = = .¹ÊÑ¡D.,6.(2018½Î÷,11,3·Ö)Ò»Ôª¶þ´Î·½³Ìx2-4x+2=0µÄÁ½¸ùΪx1,x2,Ôò -4x1+2x1x2µÄֵΪ .,´ð°¸ 2,½âÎö ¡ßÒ»Ôª¶þ´Î·½³Ìx2-4x+2=0µÄÁ½¸ùΪx1¡¢x2, ¡à -4x1=-2,x1x2=2, ¡à -4x1+2x1x2=-2+2¡Á2=2.,7.(2018ÄÚÃɹŰüÍ·,13,3·Ö)Èôa-3b=2,3a-b=6,Ôòb-aµÄֵΪ .,´ð°¸ -2,½âÎö ÓÉÌâÒâµÃ(a-3b)+(3a-b)=8,¡à4(a-b)=8,¡àb-a=-2.,8.(2016°²»Õ,18,8·Ö)(1)¹Û²ìÏÂÁÐͼÐÎÓëµÈʽµÄ¹ØÏµ,²¢Ìî¿Õ: (2)¹Û²ìÏÂͼ,¸ù¾Ý(1)ÖнáÂÛ,¼ÆËãͼÖкÚÇòµÄ¸öÊý,Óú¬ÓÐnµÄ´úÊýʽÌî¿Õ: 1+3+5+¡+(2n-1)+( )+(2n-1)+¡+5+3+1= .,,½âÎö (1)42;n2.(2)2n+1;2n2+2n+1.,9.(2018¹óÖݹóÑô,17,8·Ö)Èçͼ,½«±ß³¤ÎªmµÄÕý·½ÐÎÖ½°åÑØÐéÏß¼ô³ÉÁ½¸öСÕý·½ÐκÍÁ½¸ö¾ØÐÎ. Äõô±ß³¤ÎªnµÄСÕý·½ÐÎÖ½°åºó,ÔÙ½«Ê£ÏµÄÈý¿éÆ´³ÉÒ»¸öоØÐÎ. (1)Óú¬m»ònµÄ´úÊýʽ±íʾƴ³ÉµÄ¾ØÐÎÖܳ¤; (2)µ±m=7,n=4ʱ,Ç󯴳ɵľØÐÎÃæ»ý.,½âÎö ÉèоØÐεÄÖܳ¤ÎªC,Ãæ»ýΪS, ÓÉÌâͼ,µÃоØÐεÄÒ»±ß³¤Îªm-n,ÆäÁڱ߳¤Îªm+n. (1)C=2(m-n)+2(m+n)=4m. (2)S=(m-n)(m+n)=m2-n2, µ±m=7,n=4ʱ,S=72-42=49-16=33.,C×é ½ÌʦרÓÃÌâ×é ¿¼µãÒ» ´úÊýʽ,1.(2018ÔÆÄÏ,7,4·Ö)º¯Êýy= µÄ×Ô±äÁ¿xµÄȡֵ·¶Î§Îª ( ) A.x¡Ü0 B.x¡Ü1 C.x¡Ý0 D.x¡Ý1,´ð°¸ B Èô ÓÐÒâÒå,Ôò1-x¡Ý0,¡àx¡Ü1.,2.(2015ɽ¶«ÁÙÒÊ,11,3·Ö)¹Û²ìÏÂÁйØÓÚxµÄµ¥Ïîʽ,̽¾¿Æä¹æÂÉ: x,3x2,5x3,7x4,9x5,11x6,¡ °´ÕÕÉÏÊö¹æÂÉ,µÚ2 015¸öµ¥ÏîʽÊÇ ( ) A.2 015x2 015 B.4 029x2 014 C.4 029x2 015 D.4 031x2 015,´ð°¸ C ¸ù¾ÝÌâÒâ¿ÉÖªµÚn¸öµ¥ÏîʽΪ(2n-1)xn,Òò´ËµÚ2 015¸öµ¥ÏîʽÊÇ(2¡Á2 015-1)x2 015=4 02 9x2 015.¹ÊÑ¡C.,3.(2015ÖØÇì,11,4·Ö)ÏÂÁÐͼÐζ¼ÊÇÓÉͬÑù´óСµÄСԲȦ°´Ò»¶¨¹æÂÉËù×é³ÉµÄ,ÆäÖеڢٸöͼÐÎ ÖÐÒ»¹²ÓÐ6¸öСԲȦ,µÚ¢Ú¸öͼÐÎÖÐÒ»¹²ÓÐ9¸öСԲȦ,µÚ¢Û¸öͼÐÎÖÐÒ»¹²ÓÐ12¸öСԲȦ,¡¡, °´´Ë¹æÂÉÅÅÁÐ,ÔòµÚ¢ß¸öͼÐÎÖÐСԲȦµÄ¸öÊýΪ ( ) A.21 B.24 C.27 D.30,´ð°¸ B µÚ¢Ù¸öͼÐÎÖÐÓÐ2¡Á3=6¸öСԲȦ;µÚ¢Ú¸öͼÐÎÖÐÓÐ3¡Á3=9¸öСԲȦ;µÚ¢Û¸öͼÐÎÖÐÓÐ 3¡Á4=12¸öСԲȦ;¡¡;µÚ¢ß¸öͼÐÎÖÐÓÐ3¡Á8=24¸öСԲȦ,¹ÊÑ¡B.,4.(2017¼ªÁÖ,8,3·Ö)Æ»¹ûÔ¼ÛÊÇÿǧ¿ËxÔª,°´8ÕÛÓŻݳöÊÛ,¸ÃÆ»¹ûÏÖ¼ÛÊÇÿǧ¿Ë Ôª(Óà º¬xµÄ´úÊýʽ±íʾ).,´ð°¸ 0.8x,½âÎö 8ÕÛÓÅ»ÝÏ൱ÓÚÊÇÔ¼ÛµÄ80%,¹Ê¸ÃÆ»¹ûÏÖ¼ÛÊÇÿǧ¿Ë0.8xÔª.,5.(2017ɽÎ÷,12,3·Ö)ijÉ̵ê¾ÏúÒ»ÖÖÆ·ÅƵÄÏ´Ò»ú,ÆäÖÐijһÐͺŵÄÏ´Ò»úÿ̨½ø¼ÛΪaÔª,ÉÌ µê½«½ø¼ÛÌá¸ß20%ºó×÷ΪÁãÊÛ¼Û½øÐÐÏúÊÛ,Ò»¶Îʱ¼äºó,É̵êÓÖÒÔ9ÕÛÓŻݼ۴ÙÏú,Õâʱ¸ÃÐͺŠϴÒ»úµÄÁãÊÛ¼ÛΪ Ôª.,´ð°¸ 1.08a,½âÎö ¸ù¾ÝÌâÒâµÃ,a¡¤(1+20%)¡Á90%=1.08a.¹Ê´ð°¸Îª1.08a.,6.(2015ºÓ±±,20,3·Ö)Èçͼ,¡ÏBOC=9¡ã,µãAÔÚOBÉÏ,ÇÒOA=1.°´ÏÂÁÐÒªÇó»Í¼: ÒÔAΪԲÐÄ,1Ϊ°ë¾¶ÏòÓÒ»»¡½»OCÓÚµãA1,µÃµÚ1ÌõÏß¶ÎAA1; ÔÙÒÔA1ΪԲÐÄ,1Ϊ°ë¾¶ÏòÓÒ»»¡½»OBÓÚµãA2,µÃµÚ2ÌõÏß¶ÎA1A2; ÔÙÒÔA2ΪԲÐÄ,1Ϊ°ë¾¶ÏòÓÒ»»¡½»OCÓÚµãA3,µÃµÚ3ÌõÏß¶ÎA2A3; ¡¡ ÕâÑù»ÏÂÈ¥,Ö±µ½µÃµÚnÌõÏß¶Î,Ö®ºó¾Í²»ÄÜÔÙ»³ö·ûºÏÒªÇóµÄÏß¶ÎÁË,Ôòn= .,´ð°¸ 9,½âÎö ÓÉÌâÒâ¿ÉÖª:AO=A1A,A1A=A2A1,¡¡, Ôò¡ÏAOA1=¡ÏOA1A,¡ÏA1AA2=¡ÏA1A2A,¡¡, ¡ß¡ÏBOC=9¡ã,¡à¡ÏA1AB=2¡Á9¡ã=18¡ã,¡ÏA2A1C=27¡ã,¡ÏA3A2B=36¡ã,¡ÏA4A3C=45¡ã,¡¡, ¡à9¡ã(n+1)=90¡ã,½âµÃn=9.,7.(2018°²»Õ,18,8·Ö)¹Û²ìÒÔϵÈʽ: µÚ1¸öµÈʽ: + + ¡Á =1, µÚ2¸öµÈʽ: + + ¡Á =1, µÚ3¸öµÈʽ: + + ¡Á =1, µÚ4¸öµÈʽ: + + ¡Á =1, µÚ5¸öµÈʽ: + + ¡Á =1, ¡¡ °´ÕÕÒÔÉϹæÂÉ,½â¾öÏÂÁÐÎÊÌâ: (1)д³öµÚ6¸öµÈʽ: ; (2)д³öÄã²ÂÏëµÄµÚn¸öµÈʽ: (Óú¬nµÄµÈʽ±íʾ),²¢Ö¤Ã÷.,½âÎö (1) + + ¡Á =1. (2·Ö) (2) + + ¡Á =1. (4·Ö) Ö¤Ã÷:×ó±ß= = = =1=ÓÒ±ß. (8·Ö),˼··ÖÎö (1)·ÖÎö¸ø³öµÄ5¸öµÈʽ·¢ÏÖ,µÈʽ×ó±ßÊÇÈý¸ö·ÖÊýµÄºÍ,µÚ1¸ö·ÖÊýµÄ·Ö×Ó¶¼ÊÇ1,·Ö ĸÓëµÈʽµÄÐòºÅÏàͬ;µÚ2¸ö·ÖÊýµÄ·Ö×ӱȵÈʽµÄÐòºÅС1,¶ø·Öĸ±ÈµÈʽµÄÐòºÅ´ó1;µÚ3¸ö·ÖÊý ÕýºÃÊÇǰÁ½¸ö·ÖÊýµÄ³Ë»ý,µÈʽµÄÓұ߾ùΪ1.¾Ý´Ë¿Éд³öµÚ6¸öµÈʽ.(2)¸ù¾Ý(1)Öз¢ÏֵĹæÂÉ ¿Éд³öµÚn¸öµÈʽ,²¢¸ù¾Ý·ÖʽµÄÔËËã½øÐÐÖ¤Ã÷.,¿¼µã¶þ Çó´úÊýʽµÄÖµ,1.(2018±±¾©,6,2·Ö)Èç¹ûa-b=2 ,ÄÇô´úÊýʽ ¡¤ µÄֵΪ ( ) A. B.2 C.3 D.4,´ð°¸ A ¡¤ = ¡¤ = ¡¤ = .µ±a-b=2 ʱ,Ôʽ= = .¹ÊÑ¡A.,2.(2018ÔÆÄÏ,14,4·Ö)ÒÑÖªx+ =6,Ôòx2+ = ( ) A.38 B.36 C.34 D.32,´ð°¸ C ¡ßx+ =6,¡à =x2+ +2=36,¡àx2+ =34.,˼··ÖÎö ÓÉx+ µÄÖµÇóx2+ µÄÖµ,¿¼ÂÇÕûÌå´úÈë·¨,½«x+ ƽ·½ºóת»¯Îªº¬x2+ µÄÐÎʽ,½ø ¶øÇó½â.,·½·¨×ܽá Áé»îÓ¦ÓÃÍêȫƽ·½¹«Ê½Êǽâ¾ö±¾ÌâµÄ¹Ø¼ü.,3.(2017ÖØÇìA¾í,10,4·Ö)ÏÂÁÐͼÐζ¼ÊÇÓÉͬÑù´óСµÄÁâÐΰ´ÕÕÒ»¶¨¹æÂÉËù×é³ÉµÄ,ÆäÖеڢٸö ͼÐÎÖÐÒ»¹²ÓÐ3¸öÁâÐÎ,µÚ¢Ú¸öͼÐÎÖÐÒ»¹²ÓÐ7¸öÁâÐÎ,µÚ¢Û¸öͼÐÎÖÐÒ»¹²ÓÐ13¸öÁâÐÎ,¡¡,°´ ´Ë¹æÂÉÅÅÁÐÏÂÈ¥,µÚ¢á¸öͼÐÎÖÐÁâÐεĸöÊýΪ ( ) A.73 B.81 C.91 D.109,´ð°¸ C µÚ¢Ù¸öͼÐÎÖÐÓÐ12+2¸öÁâÐÎ, µÚ¢Ú¸öͼÐÎÖÐÓÐ22+3¸öÁâÐÎ, µÚ¢Û¸öͼÐÎÖÐÓÐ32+4¸öÁâÐÎ, ¡¡ µÚ¢á¸öͼÐÎÖÐÓÐ92+10¸öÁâÐÎ, 92+10=81+10=91,¹ÊÑ¡C.,4.(2015ËÄ´¨ÃàÑô,11,3·Ö)½«Ò»Ð©ÏàͬµÄ¡°¡ð¡±°´ÈçͼËùʾµÄ¹æÂÉÒÀ´Î°Ú·Å,¹Û²ìÿ¸ö¡°¹êͼ¡± Öеġ°¡ð¡±µÄ¸öÊý,ÈôµÚn¸ö¡°¹êͼ¡±ÖÐÓÐ245¸ö¡°¡ð¡±,Ôòn= ( ) A.14 B.15 C.16 D.17,´ð°¸ C ¸ù¾Ýÿ¸ö¡°¹êͼ¡±Öеġ°¡ð¡±µÄ¸öÊý,µÃµÚn¸ö¡°¹êͼ¡±Öеġ°¡ð¡±µÄ¸öÊý¿É±íʾ Ϊ5+n(n-1),µ±5+n(n-1)=245ʱ,½âµÃn1=16,n2=-15(ÉáÈ¥),ËùÒÔn=16.¹ÊÑ¡C.,ÆÀÎö ±¾Ì⿼²éͼÐεı仯¹æÂÉ.̽Ë÷¹æÂɵÄÎÊÌâÊǽü¼¸ÄêÖп¼µÄÒ»¸ö¡°ÈÈÃÅ¡±ÌâÐÍ.½â¾öÕâ ÀàÎÊÌâµÄ»ù±¾Ë¼Â·ÊÇͨ¹ý¹Û²ì¡¢·ÖÎöÈô¸ÉÌØÊâÇéÐÎ,¹éÄÉ×ܽá³öÒ»°ãÐÔ½áÂÛ,È»ºóÑéÖ¤½áÂÛµÄ ÕýÈ·ÐÔ.,5.(2016ºÓ±±,18,3·Ö)Èômn=m+3,Ôò2mn+3m-5nm+10= .,´ð°¸ 1,½âÎö 2mn+3m-5nm+10=-3mn+3m+10,°Ñmn=m+3´úÈë,µÃÔʽ=-3(m+3)+3m+10=-3m-9+3m+10 =-9+10=1.,6.(2015½ËÕËÕÖÝ,16,3·Ö)Èôa-2b=3,Ôò9-2a+4bµÄֵΪ .,´ð°¸ 3,½âÎö 9-2a+4b=9-2(a-2b).°Ña-2b=3´úÈë,Ôʽ=9-2¡Á3=3.,7.(2015ºþÄϳ»ÖÝ,16,3·Ö)Çë¹Û²ìÏÂÁеÈʽµÄ¹æÂÉ: = , = , = , = , ¡¡ Ôò + + +¡+ = .,´ð°¸,½âÎö Ôʽ= + + +¡+ = = = .,ÆÀÎö ±¾ÌâÊôÔĶÁÀí½âÐ͹æÂÉ̽¾¿Ìâ,´ÓËù¸øÐÅÏ¢ÖÐÕÒ³ö¹æÂÉÊǽâÌâ¹Ø¼ü,ÊôÖеµÌâ.,8.(2015±±¾©,18,5·Ö)ÒÑÖª2a2+3a-6=0,Çó´úÊýʽ3a(2a+1)-(2a+1)(2a-1)µÄÖµ.,½âÎö Ôʽ=6a2+3a-4a2+1 =2a2+3a+1 =(2a2+3a-6)+7, ¡ß2a2+3a-6=0,¡àÔʽ=7.,A×é 2016¡ª2018ÄêÄ£Ä⡤»ù´¡Ìâ×é (ʱ¼ä:10·ÖÖÓ ·ÖÖµ:15·Ö) Ò»¡¢Ñ¡ÔñÌâ(¹²3·Ö) 1.(2016¸£ÖÝ¡°Öн²Ä£¡±,3)ÏÂÁжþ´Î¸ùʽÖеÄ×î¼ò¶þ´Î¸ùʽÊÇ ( ) A. B. C. D.,´ð°¸ A =2 ,¹ÊB²»·ûºÏÌâÒâ; =2 ,¹ÊC²»·ûºÏÌâÒâ; = ,¹ÊD²»·ûºÏÌâÒâ.¹ÊÑ¡ A.,ÈýÄêÄ£Äâ,¶þ¡¢Ìî¿ÕÌâ(ÿСÌâ3·Ö,¹²12·Ö),2.(2018ÁúÑÒÖʼì,11)ʹ´úÊýʽ ÓÐÒâÒåµÄxµÄȡֵ·¶Î§ÊÇ .,´ð°¸ x¡Ý2,½âÎö ±»¿ª·½Êý·Ç¸º,¹Êx-2¡Ý0,x¡Ý2.,3.(2016¸£ÖÝÆÁ¶«ÖÐѧһģ,14)ÒÑÖª×î¼ò¶þ´Î¸ùʽ Óë Äܺϲ¢,Ôòa= .,´ð°¸ 0,½âÎö ¡ß =2 , Ϊ×î¼ò¶þ´Î¸ùʽ,¡àa+2=2,¡àa=0.,4.(2017ÕÄÖÝÖʼì,15)ÈôʵÊýaÂú×ãa2-2a-1=0,Ôò2a2-4a+2 015µÄÖµÊÇ .,´ð°¸ 2 017,½âÎö ¡ßa2-2a-1=0,¡à2a2-4a+2 015=2(a2-2a-1)+2 017=2 017.,5.(2017ÈýÃ÷Öʼì,15)ÒÑÖªm+n=4,mn=2,Ôò´úÊýʽ3mn-2m-2nµÄֵΪ .,´ð°¸ -2,½âÎö ¡ßm+n=4,mn=2,¡à3mn-2m-2n=3mn-2(m+n)=3¡Á2-2¡Á4=-2.,B×é 2016¡ª2018ÄêÄ£Ä⡤ÌáÉýÌâ×é (ʱ¼ä:20·ÖÖÓ ·ÖÖµ:30·Ö) Ò»¡¢Ñ¡ÔñÌâ(ÿСÌâ3·Ö,¹²6·Ö),1.(2018ÏÃÃÅÖʼì,5)Èô967¡Á85=p,Ôò967¡Á84µÄÖµ¿É±íʾΪ ( ) A.p-1 B.p-85 C.p-967 D. p,´ð°¸ C ¡ß967¡Á85=967¡Á(84+1)=967¡Á84+967, ¡à967¡Á84=967¡Á85-967=p-967.,2.(2016¸£ÖÝ¡°Öн²Ä£¡±,7)ÈôaÊÇ·½³Ì2x2-x-3=0µÄÒ»¸ö½â,Ôò6a2-3aµÄֵΪ ( ) A.3 B.-3 C.9 D.-9,´ð°¸ C ÓÉÌâÒâµÃ,2a2-a-3=0,Ôò2a2-a=3,¹Ê6a2-3a=3(2a2-a)=3¡Á3=9.,¶þ¡¢Ìî¿ÕÌâ(ÿСÌâ3·Ö,¹²9·Ö),3.(2016ÕÄÖÝÖʼì,12)Ò»¸öÕý·½ÐεÄÃæ»ýÊÇa2+2a+1(a0),ÔòÆä±ß³¤Îª .,´ð°¸ a+1,½âÎö Õý·½Ðα߳¤Îª = =|a+1|,¡ßa0,¡àa+10,¹Ê´ð°¸Îªa+1.,4.(2017½ú½Öʼì,13)ÒÑÖª(2a+2b+1)(2a+2b-1)=19,Ôòa+b= .,´ð°¸ ¡À,½âÎö Éèa+b=x,Ôò2a+2b=2x,¹Ê(2a+2b+1)(2a+2b-1)=19¿É»¯Îª(2x+1)(2x-1)=19,¼´4x2-20=0,½â·½ ³Ì¿ÉµÃx=¡À .,5.(2017ʯʨÖʼì,15)ÒÑÖª¹ØÓÚx¡¢yµÄ¶þÔªÒ»´Î·½³Ì×é Ôò4x2-4xy+y2µÄֵΪ .,´ð°¸ 36,½âÎö 4x2-4xy+y2=(2x-y)2, ¢Ù+¢ÚµÃ2x-y=6,¹Ê´ð°¸Îª36.,Èý¡¢½â´ðÌâ(¹²15·Ö),6.(2018ÄþµÂÖʼì,22)ÈôÕýÕûÊýa,b,cÂú×ã + = ,Ôò³ÆÕýÕûÊýa,b,cΪһ×éºÍгÕûÊý. (1)ÅжÏ2,3,6ÊDz»ÊÇÒ»×éºÍгÕûÊý,²¢ËµÃ÷ÀíÓÉ; (2)ÒÑÖªx,y,z(ÆäÖÐxy¡Üz)ÊÇÒ»×éºÍгÕûÊý,ÇÒx=m+1,y=m+3,Óú¬mµÄ´úÊýʽ±íʾz,²¢Çóµ±z=24 ʱmµÄÖµ.,½âÎö (1)ÊÇ.ÀíÓÉÈçÏÂ: ¡ß + = ,Âú×ãºÍгÕûÊýµÄ¶¨Òå,¡à2,3,6ÊÇÒ»×éºÍгÕûÊý. (2)¡ßxy¡Üz,ÇÒÊÇÒ»×éºÍгÕûÊý, ¡à + = . ¡ßx=m+1,y=m+3, ¡à = - = - = . ¡àz= . Èôz=24,Ôò =24. ½âµÃm=5,m=-9. ¡ßx=m+1ÊÇÕýÕûÊý, ¡àm=5.,7.(2017ÏÃÃŶþ¼ì,19)ÒÑÖªmÊÇ·½³Ìx2-2x-2=0µÄ¸ù,ÇÒm0,Çó´úÊýʽ µÄÖµ.,½âÎö ·½³Ìx2-2x-2=0,Åä·½µÃ(x-1)2=3,½âµÃx=¡À +1. ¡ßm0,¡àm= +1. =m-1. µ±m= +1ʱ,Ôʽ= +1-1= .,