Toán học và tuổi trẻ Số 136 (2/1984)

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Sau đây là tài liệu Toán học và tuổi trẻ Số 136 (2/1984), mời các bạn tham khảo để hiểu rõ hơn về câu chuyện hình học giả Ơ-Clit; việc so sánh một số với nghiệm của tam thức bậc hai; đẳng thức có điều kiện trong lượng giác; một lớp bài toán hình học.

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Nội dung Text: Toán học và tuổi trẻ Số 136 (2/1984)

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:r =l-f--i- i- t lliuir rlE (,h6 qir:di dnng Gidi. ViEt. phrri;ng , ?.r +-i .? -1 thi ]rii loin iCr'ilrtrg trroug tt-r v,.;ri bii toAn -t 'lr'rlrg vi du 2 Xdt lilrn g: -- JJr l ;n6c6 r'* 1 iiao: h* rn 'ljr**2r*3 -! lt - (f," - r)* t D / llttt s: - vQ'r, n6 r:6 bing bi€in thiEn.- 11 btttl / \ , a, Oil thi tri:rr hinh \e (lru Ilil.t\ l9'n-(, '] -- . , Il, ..:: ti -i-:? ^5 tric Il 3r.'i { .! .\ :, fi drr 5. i , nr trt ,l? i', !:r r a:t g tthet, re r:hi ciin liip h&ur: bi6n thiin viii 0 (.r: ' t;i l'' l- .i I lli :' ( t). fu'bing brin thi6u ur-r- isei cAc g-iir tli cira v'vdi 0 ( is,:< ti, ta sirr: r'a li€t quii piili cit il rthilt rngi ngl:ilrrr r lri'i I inr: nr ) l. .* - '14 !nin - l) -- ls>in *3)(n-4i ffiI B&ffi /a(n-1).-19(5(n*3i ( nlo [ri #*rrrc
I .. . :, f*+c=o {^{ '['rr I h5'r Nhu vi:', db tirn r:gtrigrl ngu-1'6n cira phuo*g r'5 ryr a t4++ s Yz{' - trinh, ta plilin lir:h 1964zu ilrunh ba srj ngtrytl; :189 (rrrotl 1Utr0) 172 lrorre ii6 , ,i hlti s,i hiin! nlritr vi' eo tirrh t h$li ' '' ' ' 16 khlcr'sd ttrLr 3, Vi khi ptr*n tieh 19ti4 ra thriu 1;{ * b21. (motl 1000) , 4'[! ++ ' etu 4,. i;8 ,-.t41 irriorl 1000) ;. 1904 = 1.2.491 1?16 481 (lnott lt-too) s fu, = Lr.t f P-t ' n6rrchi c6 tlrb phAn lich 19643u th6u mirr 36ir = ,\ )72o , 6ol (rrrorJ i000)' cau lrCn Ihco ciLc clc]r siru rrFn: l7l1l0h j i (rrr,,d iflt:0) .' 1r\ fi) r-Fu = zto.4ot* 2m 1734 - . Itl.(rrlocl tC00) {F +t= l2o - Jg (2) "*i . n? = 0,. 1..,, Jll 'l rr {'1) .r :r (2 ) su v lr l nn ; - t : (:i n: t-l "y+ -'.2'" -4'.t1"' 2000 elfri .. l=19i20-2- *l m = 0. !....,10 I 984 .-'1i'- ( (3i i s+u J4$ l'o .tg8;*"" ' -121 (moit 10{JU). er,r" ,. .' t, ( r - g+1:4'r120-!nr.24c tlrc la uir dlltt so lau {'ltng \:uJ " .,- do ln. 121. ---/ f s(J A t)tft n1:flr: {,.,.,i 0 N.D.V o. f, .., ( r*u=-491n' ---1 \4/ 4e I .,,-r* I =lgl20-2t.240 BAi'4/133. Clto. n s6 tt! rhr'dn oi, a2,.,.: a.n, rl1' -0,,1,...,.i0 (irii c{c hg plrLrorrg lr!rrli lr'0n (la r6ug-vilc l) ail:. 19Ei ed:i,ntoa ii1,2...., rr; q ua dun giirr) t:r si' ' rluoc J4 rrghigrrr ngu.r ilrr l) BSCffN (rit, a;) ]> 1(i*; t'ai net i, j.x 1,.,.,n tltro'ng cira phu'ong trinh tl6 cho,, .. va tf I,' J P.(t G. d .," Chb:ng railfi rdng : ' BAi ;ii I33. ?im lla cirii sd tQn aing'efi.a sd , I.bt et/lt,f'a tle}' r'irrg, ndu .'ti rrgu-v€r e'thda ' ; I t985 ) 1u.:ij/(nr + l), ,i do nr Ia s6 nrarr l'Jb3. rrr b n -rnt t,; ,rr,ieri'"thi co ch;rn 'quiL boi .sd ciraj,o Ii.: o, 2a,..., aru lih0ng vutlt 1983. Vi viy n€u' k-r' hiqrr /r1 ii ;6 .crc si, llorrg ti'p a * loi, t1'83 Lai B{t!i.(cfia ,Vguyin Tiin Dilng, Ao10 DI{TH dB, ... .rn I t iro,rg vu,.,i irtt& 1983/j rir ltin hon,' Hd NQi). \'il. 1985 la. rndl. sd l6 v* chiu }6t uLt.r isas/f j-+ 1), vdi:-; = x,2; .;. 1s82/ ti;i trrlri d6 tLeo 5 nerr tr6rr ta c6 i j,. ,: 2000 -. - : i'I * 2fte"1- .., -{- jAi , {. '/ + .-' 1 986 li sfr c'ir.c sai la Lr6i cira it nhi I rndl s6, lliuoc tf p. 5(2ir'l t)(k € JY). : hgp A rrra kh6ng vrrol rltri 1C83. \lrirrrg do diEr-r' Suv ra : I
,t.:..,-lt .. i r,iL chir l' kr * l:r * -. * lrj [ri (,nr rili Iy' (*)l ( [rr {r)l x ta c6: q r: l/ioI l.r.-rl + l/'r-r)lx ol ur) 19S3 l + I:t'-;c *"4,. l BA1" gif i* rhirlg nr.infu r: d gS:" 'lilrlrc r[1- t...-..".-..-i sE gi&siir cri p sii thu6c.{ * } ct,....rrn lr-i i i,:.,..,99.1t lzl ,^t Kl:i tlo si cu p btir sii r-ri:a eire sd nay thugc -r iJ.' .-rl , f J -.1 ,i:-1'
&;t:.:' T: jj1s=ffi] ::i. _ri*t!i- :1 L ':.:.r [' : I tr i I i Tti P (0) ='3F (l)--- 38 {2) * P (3) ta e6 Phfln ticJ: lroiil toi-n lnoirg tq ia ciing c6: I 3 P(1)-P (o)+ 3P {:i : P (s) = 3 * c x16 . r) A P r (sa Bu .b Sec}r) . (gl 3*cr * r-.2n-3 .: -)a-p(t):a* ilc , .;- C0ng (1), (2), (3) r,d'theo vd ta dunc: Nhrt v{,1' vrii 1 ( {.3, n ta lcri: . .s * p{3) I * lo * ll3.-lt^3* i tr A. EC+ ${5.'C.{ + yC >4S.166, AI} ding thirc x&v ra.lilri vr.r chi khi If Ii tnrc t{lr a3 ,'l t _ o ri,i = ts -..i*q r?= r / "t . r,r^_31 cfia .taur ginc dIJ{1. Yn1 dibu:.cLn tim },I li lrqc \ la - /, (I)l - J-i:-*.- \/1 , ltinr cria 1am giAc .dBC1 t I i) t [r'PiO1! =1r::i .I 1. b) 'l'arn gi6c Afif, ("1) goe tri 14i .4. i I(hi d6"tia ihilc P {c) r,rl lirn e''i c6c i$ rrr'i 4 d.8,C Ia n gh if ,rr ciia lr,' : (,lx + 3 B + (. : 6o? - i2,r *3 {l-l+zB+c -2trE--larl { Cao-I ( r;-r'* t ++ { tl B * 5o= - 'r,rZ 'i- {24 *'l (tt i-:it:u-:r,*-iu*{ {t=,, d tlirrh 'i '' +- {E ll = (- {i,ir 'i ?ri r !tl,;r; (:i) -,tt:' giri: viri .1C viL 3ll'= '1jJ' Gie .l I tn - irr" - 11),'(j. 'Kil vutllg I = A vi .${ r:iim troitil ianr giAc '481C sir 31'khitL: Yly cla;Lhirc I'(:r) = cr2 + Br -i- C t'ti A' ii,C (ndu irhringlh€ ta kii ai;' -[* dl]' r'rc' : c(l li clr{'irg x{c djnh bi}i (3) sd kit.u ciro trii rrir ti.c s'..r ti'nlg n-rinh lrtctrg tr.l'.)' (*,r cleu'nlrr'r !rurr l. D.I}, K, ' -.'- -;='. "/_\ + MB }-, J16' cs''si.isgi'-+ cB > cB" va Yn5,-ll;t i){: 'l $ll}. {.1 4- i,tc . AB> MA"ts'C '. -l. . Bai 7/133. Cfto inrn tlfu ABC, ?"im di?m ,lf ri , lrong larn giat sao iJio &J.{,r'j{,- + rUJ.iC + MC'-'til AC.;dE'+ tli:.ili3' i 'u,r.'. l4;l' lr'Lruug irqp a) ilqt gtd b! nhi nhdt. ffA.J.l,C +" Hr.. AC + ff{) .,{IJ, > Lo't gidt (eiia Yd Iiia ?-tttii-- irrl: 1)E, PT(-:1'' 4 S.\B-C : 2.:',/l' . :lC - 2'18 ' AC' Qur \hori). Iiv ireng tlul;ilg hrril ri:iv 6|i|111 cir;r 1in: p'rll '11 1a a) Tam giiic ABC c6 l:a aoc tiltort h.q-v la itiu ,iiiil, .+ riiLL g itA( RtI 't t:Ii) Tu'gii thidt suY. ra' ' hay tr{:t . $C> 2 (SlnM + s-rCrr) (1) Y a1 = (b + a .", q) 5in(,.112)
I -! a t) d'= n /l - SlSr Liti Ei&i.. 1) Tr c,r | ' l: '::'. 51= 3sBr. -6rCr. {,'rAr/(4 ft)r ' S =;iB . 8r:. Cll(4R), si ArBr BtCt ctJt I AI} BL CA D6 rhd-v l:ngt u! A,ElAil Uinh 5 ArBt iBr le+ ---_.- = :- a* Tuong trr ta ctng e6 i h,t) t)-, ni-=(h*c-a)-s in2 (..fl:) AB IA' 1" , =(b+c-a)1tt- cos lli2 BTCT ICl CLAT IAt ,:. r | ,/ b2+cz ^\ BC, IB CA IC =_!i = -.(b+c-o)"t 1----------- I Zbc I -:5--*, \Iiry la cti .I slis = Ittl te. IEtlIB. ICtitC 1bc ^ + /\Cllz: ;/_\ 2) fa c6 ICBI * G BrlC + IBL = BtC. I =_,__ lbz_(o _ _6 _ orr I I-ai cti LQnrct can va ,t,{tri}:G tbc "a)l_I*: . ,/-\ /.\ //__\ X6t 41.41C c6 CIA| : (A +.C)/2 = A1CI. llAt t,it'lr lroan lorlrr iir.urrg li.r I;.r (.() : ' V+y AtAtC cfin, l6n l-rF= ? .), -'=+ A "o 4 BtcloBt = It: !IAt b; ( o,'/ 1^ , j .- -:- D,r/ t. t'AtC,.ut L',stot; +) Idrllii= IClBet: - ICIIBt (2) hlri do: Chir -i' Arrlc ut: fslr{B . ( , I, * \cl/ { }-), \t,1 i [-:- \c;,/ \' ,,,, il:t4L V ').2 z al bl cl .'I'ti (2) va {il) ia TCIIBT=IBIICT c6 (3) : I B.tC z I.Bt.ICie /e. r-41 - (t.rriZtt2 ca -_- rq - ,ro ". l! /--;T? -_.-_-.: l') : n! IA. rB. ICi\tAt. IBt. IC|= fit6/5r (ttreo- U i&c/4) (ar! t) (abl4\ . phdn l) , I.9.7' *. Sai 9i t33 i'pe1;"9 tam gidc ABC, cde dtbnq vi L4 .IAt:fi2 -1d2. ncn Rz - a2 = ,12. sls{ phfrn q:dc cdt nhau tai I ud t'dt du'b ng trdn ngloai o :,n /1 - s/s idpcm). tilp L.AB:: lb.n last tci ,{1, ltt, C1 Got,S, g1 p6i T ;\ lreln ret : b4n l{gugdn 7 hanh Qudn ( l2P, trudng dttr*ngtng lddidn tich A.a.BC" diCntich AdrEirCr t;l'f il vua hgc vua ldln Thri Eric, TP Hb Chi uA khod.rig cdch tdi t d?n tdm drrlng {rdn ngo{i Minh) c6 l,ri *iai tdt. f rap a,rsc r.v,T.. rdac : ,/ :.. t'Br ICt Sni t0llSlj hinh chcip tr': gitic d|u S,dBCD. C^tro tt) IC Trin cqnh SC tdg dibm Ct. ' Cltring ll inh-rit,g trong.cqe tht'it di|n {qo fftdnrt 'l:c.' d.a m(t pft8ng dt qua ,.tCt.'cdt .sB, SI,, liti trtitl. drfn song sarig udi BD'td lhtAt d$n.nki nhdt. 7'inh tli€n tich thllt dt|n nhi nhd,t il6 n6u_c0nll clitg ltinh cltrip bdirg 1,, cctnh be n bdng '/5- ,* (,;,- |* :i/S7:j. Ldr qir.i. Goi .8i rir Ot tuong ung li giao cria phing cli qua.dC r.di .SB vi .tD. SfI ld dudag nrq,t cao c,ia hinh ch6p la f/t Ia giao cria , S'f;l'vdi thict c1iQn. Dc chri'ng rnintr atutc ndu lfiitit'di+n
t, song song .vai,bfi thi tallr gi6c '.SBtI]a cd diQn tich nh6 nh{l, vi. do tl6 ch6p S.{,B1Clla'c6 tht tlch nlr6 thdt. Trong khi d6,duirdg ca
WT ,-T:;,rj.:-* .r{i{:::."S-:, i::tF':::!= -,.,'-.. . .-.f: . !} H0C SI\t':rr Tirt II'rr 'nAr rrr'a E&i 1{i/136, {.,$o larrr giiic $lt{"' e6 c6'c c-4rrh a, }, c' i-hirlg rninlt' q'j-r* aoc ( :--v1t ----\' -{ AIJC \ ,'r.,lg.t i coiu8 * rotgC I tc__tg "2 2 2 \- ' l, ' Ld Van Nirr Hfni .:. (13E chu5'0n Toin Virrlr Phii) Tim hi6'u s$u t}lOm to6u h9* Xthb thdrrg Pfi.rq* .$E{tI* E*'ffIflU KIEN T RONC LIJSNG GIAC N0uYf;N Bf,uc 'ruuiu , Td {,-,i drir,,r iJriie c('t {ti|u liirt lron'i tuEng gidc Du r1o, ta co: E ll nl;ii,:r1 rlinr: iL*c g..iirn titc hirtrr .sd lugng s,inl, = sinu/nr, c,tsb : .ntosa,/m, giac citrce tlt,,:r lirirl rr' j tri 'L ''ii rrlrir*q 5i'' t.r'i t'lrra ' sin2l., + ,ror?t, = siu2a/rnZ *n?""5?orlml. nhdn ilttce r:,ia i15i sJ tiiing thcii ehin tliilu hiQn ring bu6c lio iio. l-"1::i:rg i::3t, cot'gcr + 1-oJil&-j" S u-r' t'a '" cotgc : cotgat:otg&colgr r-oi a * b * o*t0o' t'a ort: 1 * ao.?L + I,Ze.rs?o thuo.ug g{,p nhiing dang- bii tip saLt : m? * 1: (rtt* 1) .cs2a. , 1. Chq f,-tr{.io "*ir ttin hd g:rr'.r r?'ii s4 itd r7')i hut cos?, * (,rz - l/: inl -t)' phdixtic iinft srr tigi li| giffa "fre.m si itt')i1t gidtc Do d6, mrit tt'otrg .circ giic 1ri cila cosa iA cfra cac d ni s6 do /;'z: 1): ;F - Dt. 2. Cito trnrre' i.r:6{ sr lida Jrd.gi$a h&ni sd !it:;riE gidc eria ddi .($ ,ri rioi ltii lirr: n&&riE str iidn ftii r''i;'rc Yi. da 3' Thinh lip' he thirt'giira ba goc irlrrln |i,rn na* sd irt'1r*g gtitr: tia t'rit tti ettc tlfri sd 't6- a, ir, e bi6t l'i,rg: eu.lgo ccrtgb * cotga cotgc * : eolgb loioc = 1, 3. Cho lrurtt sry iidrr if t'i$c i:iinl s'# irr-c,rg gi'{c Gtd.,i.: lihrln ea1 hai r'6 ,1&ng thut dE cho vfi crln ddj sri un li*i sr,r lictl i:9 gir?* cili;r.1 r:h&,:6 tl6l sotlit u.u... tgtrlgbtgc =F 0, ta eo: l'i dtt 7.ilhrir,g tittnl, tit-"i ndu ( i * r'l=;i I ihi tge $ igl + tgri = tga tgb tgc (t + rge) (r 1 tga) = :. ''.. 4 igc + tgl, stga (tgb tgc - 1) - * -tga =(tgcltgb): (1 itg&tgi) ' Cidt. Eb cho lS tr{i ciia d3.lg thirc cin chirrrg '= + tg (-0) : tg (l-, * c) minh c6 irghia ihi :,, I; * fii: + E3t. \'i { a * b) =+ a * b * c = l;Jt. Nhung vi tr, b, clliSgr'rc n1t9u n6ry0 { e* b { c tg (a,* b) = I "'* (igti {- tg})/(1-tEaigb) = 1 { errl:, vi ]a c6 c * b "l- ' '* ig# -1- tgt/ :l- tgrrtg}$= 1 "::, _ .^ Sau dfiv,, lir rrF-u rir. nidt stI i'i dr1 r'B mQt lodi + {1 _r ts{l) {i * lgc} :2. d&ng ttrrlc ilii:u kiQo (I:Lc bi6t irc)ng lirr.)ng,gi6c' Yi dt.r,2. Chir;rg nrirrlr liirrg rli;u sitra = tnsittlr i'I'a'goi cho gon loai tlirug thuc dd Lit.drt-nii thizc vir tga: n tgO fiii m$t gli,tli cira cosc s€ iii *on|' tum gtic, D6 li nhltng tlang thuc gilta ciic "l/lun: phen t& ho{e efic hdrrt -*.6 lngng girie cira g6c = 1r: (n - r) irong tam gi6c,:' Chia yd vtri ve c[{c ding tiruc. dh cho , Yi de 4- ilrir,,g minh i{ug' trdtt A' B'',C 11 ,ba ' c6c trons ntdl Iilru giire tlroa urAn di'Cu liiQn \ i:.. 'ta c6. cosd = {m/n) coso. 3l;o);;:i" ia;, I "i''t.i:i=r)iir,,r i*s = c = 6uo \t0 \ \
&Ar. Ta cd tu d&ug thirc dd chol: Ta bjdn ribi srn.{ g srnlt J- sinC 1l A-B rt+B\ = sin-l * siu* f s:n (rt + Il) .2 \ -tcos 2' -cos*_-_-lX . 2 t : ,Lrrr .,, + 1, ,. .. ,--- -B .1 I :, 1,i., J x Sln *=-l 28 '',\ 'L B -i.'jnl- I .o. e-a - sin c\ sin C1, .? \ , -J 24 -& -t B n D{t t = sin (C/2), ra c6 ptr"uong triah bge hai d6i voi l: _g dB ,'1 .2 I -COS 'l* "-'.. = 0 2 ,4 'l'i bi6n _rl,ii sirr 2.{ i si.n ls -{- iin 2a; ^ r A.-B l. ,=2sinlccs-t ,+ 2s;n($+{jcos(g - C) i '2 = fs.rr^,1lrrs.i l. f .ir:-ll.os;i.,..C) i_ ,d I a.-s * 2sin.1 [co,,,t -i- crrs{Ji - C)} t vi cos l- (rnenA{0, : Iisit.4[ : r:rsi s -.1_{.,i-j:,:.,s{g *..c)] l2 : 2sin,.t . ]s :r i:j.s {- = .isi l.,i si n Bs i illl' ; ! r': rr6 cho ptruong trinh Li: lrri c6 n;Jiriim ihi ,7 ii Jl A_ A e0 tric ld cos _*' A_ D -B- : 1 {cos__+_1 i:1::: 2 2 l: {.' '.I"ndu bing - I thi A-.8.= lS.Eriiu nir;,'hLi:ng ' slE --"- t:|:i --""- thb c6, vi ,4 vir B ld go, eria nrdt lrrn giac;. 2, Khi do, La cbtt2 - t + l/.tr = 0 ruc (r*t/l)e = 0, Do do'i!) 'ruotg rlrrorig rii i , v+y :' I = sin tCl2) = tl2 /1 4l.t Jt /,1. . ,l 15 r;- a1'., "._ 4:-ts (: \, - :2t'' -- vi co-s --J_ : 1 n€n ;l*j? 0" : 2, .: ){ * ii;iri -.1- gi;: --B rilr ..- c\ f i, 2l f: g. iri'c ,1=3, \ : '.2 Nh* vAy, inm giAc -t$r) la t*rir giic cir: I'i c6 '3/jC j-f- m0t g6c bing-lE13 n6h no la tam gi4, .li.r. Ta iiiri;,, r'i:rg .1 iros-i ..: Llrs 0 vi ::':1,1 Vi d,l 5. Chung minir rXng, mdt tam gi;Lc.4BC li.,d}u khi r'4 chi i
-i : : f I :::,:. l'.-.4 t:, :.i:..4.1:::! :: !!1's Gldi. Ta goi ba canh cirn tanr giic lA a. a*d, ,2) .o.8,r..* ,'or2b.* cos?c a*?d. (rl D ul t n gdc ddi di(rr r:rt i canh (a.Fri) ' = 2i,os(rcosb""i". l{ B. 'lirco d!nh lf huur sd t.osinr. ta e6 : Z. ihri'ng' rni{rh- r,ing .n6u tga e f ig} thi siu(a*6) = 3sin(n*b). . (oiale =,o1 + (o"+ :a)z .-. ta(o * 1d)cosr ".. 3. Bi0t ring sin(4u * Ir) : ?sinb,. cor, * 0, ,2 +z *d, + d2 :o2 + o. + Jdz + 4ad.-- 2(o ?+.:ad)co sE gos(a-t-D) * O, i,tu tirrr srr ti..ri h-o giirri tg(a1b) t, -" '" va lga. ._ t.'rr**rid*3ds oz +2od+idl ,, . coso*cosb Vi ,2 at2rd } 1 nerr co eb U2 thi cd mot gi.1 tr'1 cir;r'ig(.r.12) ld tj(di:t,)rg(bi2). 5.'Thinh l4p c{e hq rhuc git, lru gr:c nhon - . ,d6: cosB )lcos0t)o. f"uf,.o e ( Otto. Do a, .b, c, b;6t r{ng, i l-i tltt 7. Cfing tninh r.dng, d6i vrri inOt tanr 1) sirr2a*siird5 J 11;26 ?sin'asinisiq:re, giirc, ndu tbng cfc nghlch dio sd. do r.i'ra hai \l = ' 2) cairh blng nghich dio s6 ilo drrcrng pl.r{n'-gi6c *D) sinc cosc. tg(ri = cfia g6c r'en^giira hai canh trOn thi.gle xen g-ita 6. Tipr 'srr lii'u lr0 girirt c'irc gric ,'ti l ii b, bi6t ! t'ang sin{rr - b) - sin?o -siu2l,. 7. Chung minh ring: t:rnr gi6c .{8L' la ein; khi ta c6 rliQt'trong cic..hQ thirc sau d?r-r,: 1i sirrC/sirrB = 2cos,l. l) 2uin,4sin 8/sinC = t'o tg(C/l). B) sin (.{/2)co.sir/2):'rrntrl2)cos3(tizr. . r.8. Chtrug milh ring {anr gi6c .lBC ln'iuOng l
\ r" tu$r}'t Lffi$- ffiAg T*-:AN S{tfxiI 6gt'tt PHAM :'NU NA Lrio r1l'r.,. gi6:i t!rii'a v6i brin cloc rndt phu'rruc Iiitl,ng dicrr"tich ciu 9800 Iirr curr i.r5 ng gS00.7f .1r lffio' phirp cri icir ciro rri;ri uLiiiu ],ii toin r irl:c :981)$3f (..rn*) nlr6 hnl disq tich cii:, hiuh rron Itinh hoc ihrrr)rrq iltrr.rc r.o i li lilritrt rniu linn kinh Ugcrrr (=gSitlgfutnr). Dr, 11, 1ire,t ngurCn mrc v{ hav g;i1r llorq cic li.\' thi ciru1.€u to*n lli 1 phiri tdn tai di?inr I nirnr tlong hinh trdn I r"i. hoi: siuii liiri. iliru.kinh 99cm r.il nim ngo:ii nroi lAn ei.n. R6 l Trirrrt tiOu chrhlg ta hir,y linr quen -vrii rri6t rlng hinL trdn tirn r ]rrln Jilnh lr.m hi lrinil tr0n I kliii riiirn mlri : riin e&n hdn Linft r' ciia mOt ftinjr I phfif1 Id idp hgp cac rtilnr ,fr6i.r ar4f pftrlng c
I r$l - ;rd lhrrg dinn liclr lhir cin cfra I00 rla qiic sE.b6 han IOtr .4f.r- lrli,jf ',.rlrr) .( tOC. +, "S,: = t:gO . < i'lr0 : i1s'{e 1r,) li tii*rrrtiih hinh r,-uOng. ftrec, ngulin Ij 1 :ririi i',', rl;i),:r'1 ii*;ii tror:!.trini r;uOngl C4nlt llt,.'nt t'r, ;l:: ,,r ;tl;:'a, i.C iC l:i;: gg1.1", .), LIO Cliitlt It t;fux eri:: hi:ri trriri pi:iri tim. Erii io;ft 3, i -,,,;; Irir,:.rr r!{,, nlii.lt kiclt thrcoc .tAy.l{} c$ i3? d::r,ir iiii,";g dd sdI .?. Cilrirgr";ninh r&ng ha,s gJn r:,iri*;r- iiri: &,ti,3.€ 2 d:r.Em n&nt trin 2 rtuun l:iiti,- itJt:tr, ,..,':,,,i1;4 ytii.lt i.!.iir;tq uttot qui l. a;i.ir.,\{it ii:ic liir: c:in J_:ri;r lqinl..i 1lt ifra nr6i filnli 3 ([olt tl ll']:Lll'l ! | l"'1), r-ir .-i:Eil'{i ddi sirng nhau grra Az, d,o t}ri diQu iich . .r4-**_**f\* 1,1 ir r..,r; ,"'rr i
r-6rn= r F.rt ': k1 . . -*: : ?rin'D*y l{inh. Vd Thnnh Nam, (tte); Nguy6n I{oa Rilrh), Nguy6n.Duy Quy.Ot (88 Blch Thugng. HoAnh li.rdng (12I); (Trung Yu'qng, Qui .\hon). Duy fit1n. LL\ narn Niuh). L€ Thanh Ht, Tiuong I-8 Thif.n T'lrsnh,(10C), l{guyEn AEh ll\i:in {ttCl), Vin Cirnls. 'rl'rinh, Ydn fii*u, FC Tro*g Vinh, (11 (An Nhcvn,l). l'hau Dri'e lliro (li lJ An Nhr"rn 2i. $T' l.am':itin, T,ir*nh }kit), Ng,r-r'r1 ir ViQt Anh Tlinh Diro (ltri€ir, LB Ouy Can, (r\n Nhcrn). tr{uirnh tio cr i:han tl1)i,(t eol, lliry6n Th6ng'l'rLing- (1i"{ IIi?u Ptrrirl ( li.\[ (.)uxng Tlulrg. Q'ri Nh,vn). Nqttltrn Ngu3'In \iirn 'l'rii, C"en LSc), (Xgi,g 'i'ir:h). I".0 'h.t iioring.TLrdn (11119 .l rnrr Qiiilc Tuirt,.QLrfrng trgli)' Lri . (lZC I' Quii,' ho,, l{rri), }iqtrri'n ilr}n (12:\ })ai Ngu;6n I{inh Son' (1tC I}hri }Ii' 1)' Pl'"snr lluv i,i'c, QuJrn,l N,rnr lli \iug). -"'qrilI'.rr "linr An 'l oin {SE LA Ltri; Qtri Ihtrn). \'ir 'l':in }'hdt' {t2I}, l-rung lrr{n ii}r.4.i (1?H}" (Phtn tlti. Cheu' 'i'::in i3A -Phan 'iirn (Jilfl Pleiku {lflf' r;ui }ihrru). NgLr-r'ln t}irc .(.li,Su .Tiridi)' ii ti i'huot:g 1)' phanr).. Ngrr.r,6n Birir ljg1rc i(hlil {{}B 116i Thrrong 2, flri fi.lrdnh: \gu1 6n \lilh \uftn, Trrin Xrifi.n (118 fleiliLr), ((iia l-ri K0rg 'l-um). Flr:lrl *inh l'larn \li{ru. Dii l)ul liiriinh' Ilu.i lh Vln 'l'hinh,.(lOC't l; Dic XIin), Bt'r i 't'lr il*a {12\i I}Lrr-irt }la T'hu{t)' ()iqtvFn \:ir 1&i, }iiia '{J}i.. li"). Ph4m '{)}ri Tliiliin 'I (ts i.'L), --l'riin 'Iif n \guy[n i)uc i{ir1' t It:C,i) ; :Bia,t ti':*, Ildng Nai), frangi. Dir:g'l rrrrrg 1''trq ( tiil Iirri'nlr'i'hiir: HLl ng' 1'h:\iih itittr, {Xgo Qrrt'd'n, Va n N in.h). Lhur l)rii ii0 R Thii tr)iiir .lr{c)i}, 1,0 Ii6nr;'l Son Cdc ttinh .(lrdc: \gtr-r.in }finh f irrin (iC CT), (tO,fs Ti{ (t*r ini rli, {Song R{}: Lt}: Ngiit' i)ng Phqn\ Cto I{hirn {i2 C'l'), ( i'hrii Plritln. 1l:ii Plrr)ng)' ti; :;rl'fr'r.q Nintr). L0 Xlir'!itrrlng' i'Jgu3'€n Nguy6r Viru Phdrc'(12 A .l'iou Yin, Quirrg liitlr)' . \qoc An, li{iir-il IIi "l'hlrnir, ill CT I;oir("X-tr}-An' i', i:litrr 'l irr:, ili) ;)'ic Tl'ri' {10'\2) Piram tr{anh Crrtingl (11 A.\ti+l ll'ri), Dii ilti Iiirsnir .11 ti;ieng). iq',,', 'r!ra't D,),' i;i1lir I\i.'r. Cal i,:1,v. 'l'iilr: i;iairli- lig-Lrfin iii-Cr rr,",g ,itfo,isin {vinti i'iii'l- }r'grt5-0. N1o:tir (i iii-r', iliiri 'i'::':i' 1'rLrin11 dlinir Can (Ji tli't,'l'lr*n Di llgii (1?'I)i {Ngd Si Lien' Yr-Ln 11:' 'l 11& 'll:r.u ti iang)' tli Bir:). Lp.u16n Vd.n Cieng (11 E [6ng ngirif p ?' ThOr:g i 12'Ciin ho Bgn dgc. ritn tdi ? rvE*T M# #rqm F$B€# B&i to6n'6i 1ti6 t:irrr lliro 'lt'irn lroc lI irii)i E,ii ciiiiig lirirr: i:iitt chirirg mitlil trrol,q ilr"rring vtri tr6 li: I n --;---- \ , -=-:*-***- (.hring ntinh ring vui ntoi si'l tr.r nhi€n- a ln c6 ,'- t.t 1/ li --'-- I i n , U (ot + l.'{nX * !i...!rrr l l) I G-.F-iil >r+ il;i { lj Ll113 1O1 glal cfrrl 'l'rin Dirl'' Li&n -- toA.f:n'ltt ItI Ndi, cldng !r0l blio itl9, t0i tir.n thAm. tiu
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