22 - +‹-±` 2 8 * 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9...

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Unformatted text preview: +‹-±` 2 8 * 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 3 3 3 3 2 2 2 2 2 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 912201 912202 912203 912204 912205 2 0 0 X X X 0 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X X X X 7 7 X 7 7 X 21 X 0 X X X 0 7 X X X X 7 3 X 2 X X 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 20 20 20 20 20 20 20 20 20 20 20 30 10 3= * ª ¶ ü k 3= * ª ¶ ü k 2= * ª ¶ ü k 2= * ª ¶ ü k 30 30 30 30 20 10 30 7 7 6 7 7 3 0 7 7 7 7 X 7 3 X 3 3 3 7 7 7 7 7 3 X X X X X X X X X X X 5 X X X X X X X X X X X X X X X 5 X X X X 6 X X X 7 X X X X X X X X X X X 2 2 X X X 2 X 2 X X X X 2 7 2 5 5 7 X 2 X X X X X X X X X X X X 5 X X 7 X X X X X X X X X X X X 9 9 6 12 7 5 0 9 18 7 7 12 16 10 2 8 8 10 7 9 7 7 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1 1 3 1 1 1 1 2 2 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 X X X X 7 0 7 0 0 0 2 3 0 7 7 7 X X X X X X X X X X X X X X X X X X 0 X X X X X X X X X X X X X X X 7 X 0 X X X X X X X X X X X X X X X X X 0 0 X X X X X X X X X X X X 14 0 0 0 0 7 0 7 0 0 0 2 3 0 7 7 7 1 + + + žz 9 0 X 70 53 5.76 ª ¶ áÀ )Ò*ß‹ u& ‹+ X 3 0 1.67 0 7 2 3.86 2 15 4 3.60 7 5 2 3.80 9 ( ‹ - `± ˜ ©* À ª · a+a 912201 ª·a¦è ABC 0 G · a M è ª ¦ MH,MK,MP0 0 (1) AH2 +BK2 +CP2 = HB2+ KC2 +PA2 (2) AH+BK+CP=HB+KC+PA ª H,K,Pè · a¦ Gª · a © h (1)AH2 +BK2 +CP2 = (AM2 ─ HM2) + (BM2 ─ KM2) + (CM2 ─ MP2) = (AM2 ─ MP2) + (BM2 ─ HM2) + (CM2 ─ KM2) = BH 2 + A P 2 + CK 2 0 AH2 +BK2 +CP2 = HB2+ KC2 +PA2 (2)0 (1)0 (AH2 ─ BH2) + (BK2 ─ CK2) + (CP2 ─ PA2) = 0 0AB(AH ─ BH) + BC(BK ─ CK) + AC(CP ─ PA) = 0 Gª · a ∵h© AB = BC = AC ∴AB(AH ─ BH) + BC(BK ─ CK) + AC(CP ─ PA) = AB[(AH ─ BH) + (BK ─ CK) + (CP ─ PA)] = 0 ∵AB≠0 ∴(AH ─ BH) + (BK ─ CK) + (CP ─ PA) = 0 0 AH+BK+CP = HB+KC+PA A H ● M P B K C 9 Gª · a ¦ è (1)0 AM0 BM0 CM0 ª · a¦è 0 AH2 = AM2 ─ HM2 , BK2 = BM2 ─ KM2 , CP2 = CM2 ─ PM2 0 0 HB2 = BM2 ─ HM2 , KC2 = CM2 ─ MK2 , PA2 = AM2 ─ PM2 AH2 + BK2 + CP2 = AM2 + BM2 + CM2 ─ HM2 ─ KM2 ─ PM2 HB2 + KC2 + PA2 = BM2 + CM2 + AM2 ─ HM2 ─ MK2 ─ PM2 0 AH2 +BK2 +CP2 = HB2+ KC2 +PA2 (2) ž h x ∵AH2 +BK2 +CP2 = HB2+ KC2 +PA2 ∴AH2 +BK2 +CP2 = (x ─ AH)2 + (x ─ BK)2 + (x ─ PC)2 = 3x2 + AH2 + BK2 + PC2 ─ 2x(AH + BK + PC) 0 3x2 = 2x(AH + BK + PC) 0 3x = 2(AH + BK + PC) ∵3x f è 3x = AH + BK + PC + BH + CK + PA = 2(AH + BK + PC) ∴AH+BK+CP=HB+KC+PA Gª · a ¨ Ø Gª · (1)Ø a¨ AM2 = AH2 + MH2 = PA2 + MP2 __________ BM2 = BK2 + MK2 = HB2 + MH2 __________ CM2 = CP2 + MP2 = KC2 + MK2 ___________ ++ 0 AH2 + MH2 + BK2 + MK2 + CP2 + MP2 = PA2 + MP2 + HB2 + MH2 + KC2 + MK2 0 AH2 +BK2 +CP2 = HB2+ KC2 +PA2 ª (2)Ø ·a ¨ ABC _ e Ð AK’ , BP’ , CH’ 0 K’, P’, H’ g H AH + BK + CP = AH’ + H’H + BK’ ─ K’K + CP’ + P’P = AH’ + BK’ + CP’ + (H’H + P’P ─ K’K) AH’ + BK’ +ª CP’Ø G · a¨ 0 M 0 BC 0 ª · M¨ NØ a AK’0 X 0 MX = XN0 0 N 0 AC 0 NP’’0 AC 0 P’’0 A 0 N 0 MP 0 NY 0 MP 0 Y 0 △ 0△ AXM≡△AXN∴ AMH≡△ANP’’ ∴ AH = AP’’ P H’ P’ ∵AP’=AH’∴ Y P’’ H ●M ∴HH’=P’P’’∴ PP’’=PP’ + P’P’’=PP’ + HH’0 MP//NP’’0 NY//AC XN 0YN = PP’’ C K K’ B MP//BP’0 MN//BC0 △MYNªi ] GØ · 9 ∠NMY =∠CBP’ = 300 Y N = MN = MX PP’’= MX MK//AK’0 MN//BC0 0MX=KK’0 KK’ = PP’’ = PP’ + HH’ PP’ + HH’ ─ KK’=00 AH+BK+CP=HB+KC+PA ª · a ¨ Ø E ÿ E Y ÿ E ÿ ` Y ð E ÿ ÿ [ OG ¾ ƒ p ‹[ ← 0 Gª 0· a ¨ Ø OQß ‹ ) á 5.76 À O Gª ¶ u Ò ‹ Gª · 70 Ø a¨ 53 ÿO[ Z‹ @ E Gª · a ¨ Ø 0 Gª · a ¨ Ø 0 912202 O± ` Z ‹ ª·a÷ © 9 Q1Q2 0 P1P2 0 a0 BC 0 ª · CD ¸ a© △ABC △ ACD Ω O ±1 ` Z ‹ Ω2 ª Ω a2 © · A P1 B 9 ,3) a P2 C Q2 D △Q1Q2C 9 Q1Q2= a 0 P1P2= Q1Q2= a Ω1a Η ª· © a9 00 Ω· 2a ÷ ª© a 00 Z±‹ ` EFGH ¸ ª·a© 0+ OH O’0· FG ¸ ª a© 0 △A’FO’ 0 a OO’’0 A’O’¸ ª· a© OO’’ H Q1 O0 9 A’ 9 E H ● a F O G A’ O 9 © ¸a ª · ±‹ `-+ R E ÿ [ @ 7 X 0 © ¸a* ª · 3 ¸a* ©· ª 0 1.67 0 (0 ‹)@ +[ O’’ ● F O’ G 0 912203 0 W1 0 W 2 0 W © 3 H ª·a W1 0W 2 0W 3 0 G· a © ¸ ª G · a ©AH 0 ª G · a BH ª © 0 A0 B0 C è ª·a© Ø W1 0 W 2 0 W 3 0 A0B0C H ª·a© OC ` Z± ‹ O± ` Z N ‹ G · a NH ª © 82035021 0 N0 0 A X1W1 X2W1 X3W1 N NW1 0 B Y1W2 Y2W2 Y3W2 N NW2 0 C Z1W3 Z2W3 Z3W3 N NW3 7 82 35 21 138 ‹O ) 0N(W1+W2+W3)=138 , N≧± 2(`Z 0N=2 , 3 , 6 , 23 , 46 , 69 , 138 N 2 3 6 23 46 69 138 W1+W2+W3 69 46 23 6 3 2 1 ∵W10 W20ª · Wc 3 x Gc W1>W2>W3 ∴W1+W2+W3≧6 ∴ N=2 , W1+W2+W3=69 ∵N=2 , ∴∴ W1 0 W3 0 W1+W3=82 →← N=3 , W1+W2+W3=46 E k 0 X1=1 , Y1=1 , Z1=1 , 0 W1+W2+W3=82 →← 0 X1=2 , Y1=1 , Z1=1 , 0 2W1+W2+W3=82 0 W1=36 Ø Gd n ª· 0 36>35 →← 0 X1=1 , Y1=0 , Z1=1 , 0 W1+W3=82 →← 0 X1=2 , Y1=0 , Z1=1 , 0 2W1+W3=82 0 W1─W2=36 , W2=4 , W3=2 , W1=40 GdnØ ª· 0 40>35 →← 0 X1=1 , Y1=1 , Z1=2 , 0 W1+W2+2W3=82 0 W3=36 Ø ª· d n 0 36>21 →← 0 X1=2 , Y1=1 , Z1=2 , 0 2W1+W2+2W3=82 0 W1+W3=36 , W2=10 , 9≧W3≧1 E ∴ 19<21 →← 035≧W1≧27 , 0 X1=1 , Y1=0 , Z1=2 , 0 W1+2W3=82 0 W3─W2=36(∵W2>W3) →← 0 X1=2 , Y1=0 , Z1=2 , 0 2W1+2W3=82 0 W1+W3=41 , W2=5 , 4≧W3≧1 E ∴ 37>35 →← 040≧W1≧37 , N=6 , W1+W2+W3=23 (W1,W2,W3)k E (20,2,1),(19,3,1),(18,4,1),(18,3,2),(17,5,1),(17,4,2), (16,6,1),(16,5,2),(16,4,3),(15,7,1),(15,6,2),(15,5,3),(14,8,1),(14,7,2),(14,6,3),(14,5,4), (13,9,1)(13,8,2),(13,7,3),(13,6,4),(12,10,1),(12,9,2),(12,8,3),(12,7,4),(12,6,5),(11,10,2), (11,9,3),(11,8,4),(11,7,5),(10,9,4),(10,8,5),(10,7,6),(9,8,6) G· d n Ø ª (16,5,2)‹ ± ` O Z 5A1C0 1A3B2C0 3B3C0 N=23 , W1+W2+W3=6 ∵W1+W2+W3=6 0 W1>W2>W3 ∴W1=3 , W2=2 , W3=1 0 A 0 3(X1+X2+X3)=23 , 0 (X1+X2+XØ 3)Ø Ø →← → ª ·c cx [a x G )¶ á u Ò À O Oß Q ‹ª ‹ N=60 (W1,W2,W3)=(16,5,2) 7 Xªa·G 0 3.86 ÀªG ¶ u Ò á) ‹O ßQ 2 Xªa·G 0 Xªa· 0 0 0 Xªa·G 0 912204 X1 0 X20 X3…0 Xn-10 Xn 0 -1 0 0 0 1 0 20O ± ` Z n ‹ X1+X2+X3+…+Xn-2+Xn-1+Xn=91 X12+X22+X32+…+Xn-22+Xn-12+Xn2=2002 0 X13+X23+…+Xn-13+Xn3 • (1)ZÿE@[ O ‹ G (2)H ª ·a ª X 1+X2+X3+…+Xn-2+Xn-1+Xn=92a Gª · ª H Gª · a ª H · iH ª[ (1)0 0 O ± a -˜ ÀÒ ‹@[i·ªG A 0 -1 , B 0 0 , C 0 1 , D 0 2 , ABCD H Gª · i [ X13+X23+…+Xn-13+Xn3=8D+C─A H Gª · i [ 0 2D+C─A=91 , 4D+C+A=2002 0 6D+2C=2093 0 3D+C= ∵· i , ∴∴ 0Gª CD H[ ∵ X 0 · X[ 2 H i , ∴∴ (2)0 (1)0 2D+C─A=92 , 4D+C+A=2002 0 6D+2C=2093 0 3D+C=1047 0i[ ª 0D=349 ─ ,G · CD H 3 3 ∵2 H >1 H ∴ H HH 20 X13+X23+…+Xn-13+Xn3 0 9 0 C=0 , D=349 A=606 8D+C─A=2792+0─606=2186______0 GaªH ª· 20 X13+X23+…+Xn-13+Xn3 0 0 0 D=00 C─A=92 , C+A=2002 C=1047 , A=955 , C─A=92______0 ª·aªH O± ` Z ‹ G · 15 H ª aª Q _ 0ª · a ª H G G · a 4H ª ª O‹Gߪ ¶)OÒ ‹ À Q áu 3.60 0ª · a ª H G 0 0 0 00 · a ª H ª 0· a ª H ª 0 G0 a ª H ª· 0 0 0 0 912205 D _¸ 0 E X[ @ ÿ H t@ (0 )ÀÒu¶ªG ‹O ßQ á) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● °[· ● ● (0 ● n ˜a±Z À `¦·ªG ‹O ● ) ● ● ● ● ● ● ● ● ● h¦a·ª 0 n h¦a·ª an h¦a·ª a19 P0─P1 → ─ P0─Q1 → ─ P0─Q0 → ││ 0 30 a29 P0─P1 P2 → │ P0─Q1 + → │ →3 0 P0─Q0 Q2 → │││ 0 50 P0 P1─P2 → │ + P1─Q2 → │ Q0 P1─Q1 →2 0 P0 ● P1 ● P2 ● Pn-2 ● Pn-1 ● Pn ● ● ● ● ● ● ● ● Q0 Q1 Q2 P0 0 P10 Q00 Q1 0 Q0 0 GQ¦ 1 h ª·a an-1 0 Q0 0 G· P¦ 1 h ªa Qn-2 Qn-1 Qn an ← 1.0 P0 0 P1 0 2.0 P0 0GQ¦ 0 h ª·a 3.0 P0 0 Q1 0 an-2 0 an-2 0 an=an-1+2an-29 n n a1=39 a2=5 x2=x+2→x2─x─2=0→(x+1)(x─2)=0→x= -1,2 9 an 0 s x1 + t x2 0 1 1 s (2) + t (-1) = 3 s (2)2 + t (-1)2 = 5 →s=0t=─ → an= (2) n ─ (-1) n ª· aª È 0G· a ª È ª 0 @ OE ÿ Z ‹ G· a 5 È ªª 3.80 0 G· a 2 È ªª 0ª · a ª È 0G· a ª È ª ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- (1)X · a` _ (2)‹ ± ` O Z ª·a ª È 0ª 100È G· a ª ·\wˆ (3)Zÿ[ p Y ÿ ÿ Y ð G [¾E ‹ ƒÿ E O EÿZ O ‹ (4)È O` Z ‹± ª¶ üih H t@ + Eÿ[@ / @@ G· a ª È ª 226 91 0 11 0ª ¶ 30)Àá GuQ O Ò ß‹ Gu‹¶O±¶ Ò6Àaü i ˜` Z ª5 ÿY` 91 0 12 O ‹ ÿ[@ http://www.ck.tp.edu.tw/0 ) •È O±‹ ` ( Z ...
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This note was uploaded on 08/14/2010 for the course 數學 乙一 taught by Professor 鄭質明 during the Spring '07 term at Fudan University.

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