23 - U˜ö0 2 9 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6...

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Unformatted text preview: +U˜ö0 2 9 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 8 9 6 6 6 * 2 9 6 6 6 6 6 9 9 6 912301 912302 912303 912304 912305 X 7 X X X X X 7 X 7 X 7 5 7 x x x x x x x x x x x x x X X X X x X X 7 6 X X 6 X X 5 6 6 6 7 6 6 6 x x x x x x x x x x x x x 6 6 0 x X X X X 7 4 7 4 7 3 7 7 X X 5 X 6.5 X x x x x x x x x x x x x x X X X 7 3.5 7 7 7 5 6 X 6 X X X X 7 X X X 7 X x x x x x x x x x x x x x X X X X X X 6 6 2 X 2 3 X X 3 2 X X X X 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 X X X X X X X 2 2 20 17 9 19 7 3 15 22 13 13 12 13 26.5 15 2 2 2 2 2 2 2 2 2 2 2 2 2 6 6 0 7 3.5 7 13 22 ] ] ª · ± b X* 7 6 6.71 )+ U @; E Ü : 13 1 5.54 15 9 5.93 7 2 6.14 21 0 2.10 63 18 26.42 9 9 ( U ˜ ö •˜ œ ³ * ª · š z 1+ 912301 6 6 ABCD AM = AN X ] AB + BM AD + DN M6 N6 ∠MAN=4506 ± Rb· ª ± b· ª ± M) b R· ª E6 AC C 6 N ˜zš· Rª F6 AC C 0 ∵∠1+∠2 = 45 A ∠2+∠3 = 450 3 ∠3+∠4 = 450 12 ∴∠1=∠3 ∵ ∠ 2=∠4 ∴△ AME~△ AND AM AN ⇒ = AE + ME AD + DN AM AE + ME ⇒ = … AN AD + DN B △ A BM~△ AFN AN AM ⇒ = AF + FN AB + BM AM AB + BM ⇒ = … AN AF + FN ∵∠5=∠6= 450 ∴ ME = CE ⇒ AE + ME = AE + CE = AC 0 ∵∠7=∠8= 45 ∴ FN = CF ⇒ AF + FN = AF + CF = AC AM AE + ME AC = = ∴ … AN AD + DN AD + DN AM AB + BM AB + BM = = … AN AF + FN AC X AM AN 2 2 4 8 F E 6 5 D N 7 C M = AC × ( AB + BM ) AC × ( AD + DN ) ∴ AM = AN AB + BM AD + DN * ª · h± Ξ AC C ∠1+∠3= 4506 ∠2+∠5=4506 * ª · h± Ξ ∵∠1+∠2=450 ∴∠2=∠3∵ 1=∠5 ∠ BM C EB = BM AE △ AEB ≅ △ AMB(SAS) ∴∠3=∠4∵ ∠ 2=∠4 AE = AM DN C DF = DN AF △ AFD ≅ △ AND(SAS) ∴∠5=∠6∵ ∠ 1=∠6 AF = AN ∵ CEA △ CAF △ ∠A EC=900 -∠4=900 -∠3=∠1+∠2+∠5=∠6+∠2+∠5=∠CAF ∠AFC=900 -∠6=900 -∠5=∠2+∠1+∠3=∠4+∠1+∠3=∠CAE ∴△CEA~△CAF(AA) AE AC CE AM AC CE = = = = ∴ AF CF AC AN CF AC AM AC AM CE = = … … AN CF AN AC X AM AN 2 2 = AC CE AM CE BC + BE ⋅ ⇒ = = = CF AC AN CF CD + DF AB + BM 6 AD + DN A 4 6 5 2 1 F D 3 N E B M C ª · xh± @ E Ü : + U; 6 * ª · xh± · ª³ + ’œU # å á * · ± h xª * 7 xh± * ª · 6 0ö + U ˜ 6 · ± h xª * 6 6.71 6 6 6 912302 △ABC ∵ E6 F H 6 P 6 Rª · ± P ¨ j c) Rª · ± k I A AP‧AB =mc2 AP‧AC C 2 E =nb 2 Da =BP‧BC =(AP-AB)‧(AC-AB) r =AP‧(AC-AB)+AB‧CB = nb2- mc2+(c2+a2-b2)/26 D6 =m6 =n6 Rª · ± F ¨ j = r6 m6 n6 a6 b6 c 6 ª · ± E¨ j r 6 (6 = a 6 = b6 = B F P R· ± I ªk R· ± I ªk PD=x6 PE=y6 PF=z PB =x +r2a2=z2+c2(1-m)2… 2 2 PC2=x2+a2(1-r) 2=y2+b2(1-n) 2… PA2=y2+n 2b2=z2+m 2c2… - 22 22 22 x -y +r a -n b =c2(m2-2m+1)-m2c2 x 2-y 2=n 2b2-r 2a2-2mc2+c2… x 2-y 2=b2(n2-2n+1)-a2(r2-2r+1) =b2n2-2b2n+b2-a2r2+2a2r-a2… 66666 n 2b2-r 2a2-2mc2+c2=b2n2-2b2n+b2-a2r2+2a2r-a2 2a2r=a2-b2+c2-2mc2+2b2n ∴ r =(a2-b2+c2-2mc2+2b2n)/ 2a26 ª · ± kI ·ÂCð R·Uªf ± ˜ j p ˜ ö` 6 R· ± k I ª 5.54Uá+ RfU· /åœ ³ ª’ R13 k I ª·± fU 1˜ ö ] 6 6 6 912303 (1)a6 b6 c6 d6 e∈R6 a+b6 c+d6 b+c6 d+e6 c+d6 e+a6 d+e6 a+b6 a6 b6 c6 d6 e 6 (2)a6 b6 c6 d6 e6 f6 g∈R6 a+b6 c+d6 b+c6 d+e6 c+d6 e+f6 d+e6 f+g6 e+f6 g+a6 f+g 6 a+b6 a6 b6 c6 d6 e6 f6 g · ± i) ª (1)∵ a+b < c+d∵ c+d < e+a => a+b < e+a => b < e … b+c < d+e d+e < a+b => b+c < a+b => c < a … a+b < c+d d+e < a+b => d+e < c+d => e < c … a > c > e > b …… ∵ e+a > c+d > a+b > d+e > b+c => a > d > b … a b cè d e ¹ ° if d < e b < d < e< c< a if e < d < c b < e < d < c < a if e < c < d b < e < c < d < a (2)∵ a+b < c+d∵ b+c < d+e c+d < e+f d+e < f+g ∴ g+a > e+f > c+d > a+b > f+g > d+e > b+c ⇒g > b a > f f > d e > g c > e d > b ⇒ a > f > d > b… a > c > e > g > b… ⇒a b abcdefg ¹ è ° ifg > d f È*· h ± ª 4 i fe > d > g f È*· h ± ª 3 i fc > d > e f È*· hª ± 2 i fd > c f È*· h ± ª 1 4+3+2+1=10 a b c d e f gÈ *± · h 10 ªh È ± · *È ªh ± · 5.73 6 66 66 · ±h* Ȫ U + ˜ ö 0 °· · ± 2* h Ȫ 6 6 6 6 6 15 œ.13 ˜U 6³ ð* + ±ö h` ˜· ª 6 6 · ±h* Ȫ 6 · ±h* Ȫ 6 10 6 6 6 · ±h* Ȫ 6 1 ȱ h* · ª 6 e+f < g+a f +g < a+b 9 912304 b· 6 a ≥ b > c > 0, a < Rª + ± ci ) b x 2 − c 2 + c x 2 − b 2 = ax 6 b x 2 − c 2 + c x 2 − b 2 = ax b=ax-c b2(x2-c2)=a2x2-2acx+c2(x2-b2) b2x2-b2/c2-a2x2-c2x2+b2/c2=-2acx x2(b2-a2-c2)=-2acx x4(b2-a2-c2)2=4a2c2x2(x2-b2) x2[(b2-a2-c2)2x2-4a2c2x2+4a2b2c2]=0 ∵ b x 2 − c 2 + c x 2 − b 2 = ax ∴x2≠0 =>x≠0 ∴[(b2-a2-c2)2-4a2c2]x 2+4a2b2c2=0 (b2-a2-c2+2ac)( b2-a2-c2-2ac)= b2-a2-c2-4a2c2 = [ b2-(a-c)2][ b2-(a+c)2] = -(b+a-c) (b-a+c) (b+a+c) (a-b+c) >0 >0 >0 >0 2 x= )6 x = ± (6 · ˆa ±ª 6 · * ˆa ±ª * ª· ˜ ·œ µ³`+ö ÿ˜U • ·Ä K ˜ 7* ˆa · ±ª 2+ 0 ˜ öU 6 · ± a * ˆª 6 6.14 6 6 6 912305 (1)@7 7 @ & Rª · ± a ˆ 6 1. Ä B Rª2.· ’ # œ ³ å +U f U 3.·öª·`œ µ³˜ ÿ *˜ f U 4.·öª` µ˜ ÿ *˜ @ EÜ;@ 8 á+U • • ○○○○○○○ ○ ○ ○ ○ ○ ○○ ` -----------------------------------------------------16 6 ○○ ○ ○ ○ ○ ○ -----------------------------------------------------26 6 ○ ○ ○○ ○○ ○○○ ○○○ ○○○○ ○○○○ ○○○○○○○○ ○○○○○○ ○○○○ ○○ (2)È·ªR ±f (N 6 2╳N Uf :ÜE@ ) ○ ○○ 6A ● ±) g·ª (1) 10 9 1 8 7 20 19 12 2 11 21 17 6 18 13 14 3 4 5 15 16 6 16 ● 2 1 34 36 35 11 5 10 38 37 34 12 6 9 13 28 29 32 33 7 8 14 25 26 27 30 31 40 15 24 23 22 39 16 17 20 21 18 19 6 26 (2)) ª· ± g fU ˜ ] ö 2fª ╳±˜·U N ˜R ö f `À ³œ· 6 ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ 1. ˜ ˜ ˜˜ 2.R· U f/³’X’Xá ª œå 3. U E Ü : @ + U ˜] ö+ “ ● ““ ”” “6” “” d ö A6 6 · ”gª ± B6 ● 6B ● 6 ˜ ` ˜U±+f À ö ª· ³ * 6 @ U EÜ: + “ ” ● d ö C6 6f ª ± È· 66 ● C ○● 1. ● = 0 →6 Rª ×n g ) 2· ± Rª · 6 g ) ± D6 D· -1g ) ª± 6D 6 D-1 2. ● = 1 →6 Rª 2×n h ·´a ● Rª · ´ 6a h E6 ª E-1 h · ´a 6 6E 6 E-1 3. ● = 2 →6 6 2×n ö ] fU ˜ ●○ ○● F6 G6 H6 (a)6 (b)6 (c) 6 6G ●○ 6 6H ○● 4. ● ≧ 3 →∵ 2×n 5 MÅ· I6 ● ● ○ ○ 6I ● ● 6● = 2 6 (a) 6 F5 MÅ· ● ● 6F ª F-1 h · ´a 6 ª· ´ 2h a 6 F-1 (b) 6 f Gö ] U˜ ª· ´ a h ª =1→h · ´a fU ˜3 ö] G-16 6 36 ●○○ ● 6 G-1 ● ● ≧ fU 2→˜À–™·ª* ˜ö ` 6 ª G-3 h · ´a 6F ●○ ○ ● ●○ 6 G-2 hhhhh ª· ´3h a ª H´-2 h ·a 6 G-3 ○ ● (c) 6 fHö ] U˜ ª· ´ a h R=1→h ª· ´ a ●○○ 6 ●○○ ○○● 6 ○○● 6 H-1 6 H-2 ª·d º„ =2→@;ÜE7 D H R· º „ d ª ●○ 6 H-3 ○ ● ddd dd ≧ 3→:ÜE@ fU 6 ●○ H-5 6 6 H-4 ○ ● ●○ 6 H-5 ○ ● ª· º „d R· º „ d ª (6 )Xp¯ 6 R· º d ª„ R· 1 d ª2 º „ 2.10 6 ...
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