Toán học và tuổi trẻ Số 144 (4/1985)

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Toán học và tuổi trẻ Số 144 (4/1985) trình bày về số, lệnh, hình và gì nữa? Cực tiểu của phân thức chính quy; việc giải phương trình đại số; giải bài lịch vĩnh cửu. Đặc biệt, với những bài tập và phương pháp giải bài tập được đưa ra trong tài liệu sẽ giúp các bạn nâng cao kiến thức về Toán học.

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Nội dung Text: Toán học và tuổi trẻ Số 144 (4/1985)

a t a a IrI r BAo nA EAt,rgAxe [IOr Kt l lr'u si: 70 'l-r]in. Hung''Eao.,.- Ila'nQi Phb tbng bi€n tQp: FlgO Sat Tir Dir. n6i z ,52;82,5 Iqi-:kEIl.,:qr*dr D * Jr{ n6UY-*N eANu ?{}.*.tr 'e: - fnONG c5c sd 139 r'i 143 cria bAo 'IHv'TT, rnxc tlrt e++ t = (;!t L )I \ U -"r:l r.a nri cing ch6 ehring ta ili tu cdctr nhin m6i vE cac sd I €lhqc quen bi6t, di d€n. elc lgnh li 'nlrfrng r,t,gi Ia r,i i chii rrg qirr lir IAnlr: ( qu:.r-\. goc gOQ r pl:6ir bi€,n dbi tr6n cAc vecttr. D6 lt nhtng lgnh i'lrieu kinr dhng Irb > r.al e Ia tQnir : ( lf,), rlgrr..vri hinl d6i xirfig rlur phAn gi6c thu nhit r, lihulg viet ttr*,nt chc blng ,11"c (: d6 u, i, , , t:h6e e;ie ban mudn bi6t: < Lg nhirng ir6ich gi ?.r-. .,1;,.",* 'I'6t lfrm! I-dng mong lmudn ed tlat dAng-quf. i. . c, rJ li c6c sr5 thuc. Tr th{y cAc Iguh dO tO 'ntriBu NS.o, ehr'rrrg ta hI_y ering nlrau ti€lp fUc kh{m ph6 , linh ch{t la nhu lin}r i: 11: -l) c6 tioh chft Ioi ich d6. * . : \l 0l Gii sii ryrgt. ++ vecto O,tI eo toa dc 16 a, b (hiflh. l) 4 it, i2 = -r. I6nh e: (? ,u, ri,ih crrdt ez = l f, l) "'/ \ ddrr a r'i u li eic veu[o cton ti tri,rr tr:.rrr: hoAnh .vh trgc lung ttri ta c6 thE vi6t : I -,& ..+- U!! = rtu 1-.but ? nlrung u Ii\ do u qual di 90e nguoc chiEu kim 'at-F-+-+'..s dEng trb. vfty a : ln, n€n Oly:I :'au * btu. Chd h'dp t:ip vi6t vb ssru tildnh (rr * bilrlvi o*b cl6i toi chr'rng tu hif,n cdn v'6 nghilt: phii dinh nghia ph6p cqirg hai If nh ti6: ' 'Dinh nghta: Ttlng cfia hai lQnh, d&. ciro II rngi &* " -... *t. * . +-:a;r*.-f,-&. .:.* & l0nli drry th{t c6 tic dung l€n moi vecto gi6ng 1. 'Y sfl nhu vj$c cfern tring. Ignh di cho tfic dgng l€n veclo 'dA cho rhi cQng (phep oQng I'eeto) h.ai #irl& * . ! .: :, 1 a rriy \ qir'-
-. _t k€t qui i4i' Ph66r ld-v tbng cria tiui lQnh tl5 ehr.r cbng i'ri phip nh{n',16i uoi cAc sd thur: (giaii gSi lA phri,p cQng trai lQnh d6' hof n. k dt lro p r .r,... l. Vdi dinh ng[ia niy'' ta co thb vidt I BAy gio tr xet rhQt s6 phi?e dang cosg * fsirrrp. ;fr == (o + ri)?. Ta rem *16 :rhu mQt lgntr vi derr; tAc dOlg l€n tr
/ i'-l 6.9a \./ CUC TIEU flUA PEIAN THUC CHf IN$E 0ur PEIAN HUY KT.TAI tldi nA3' rin giiri thiOrr rn6t l6p hdm sd HOtsG Thi du. c&c th&nlr phhn cia ;rhfrn thirc hai bi6n rlqc biQt, mil r,iQc tim cr.tc tiBu cria n6 tAt {S 4S I :-2 tlc n giin do ciiu. tr(rc dic biOt cfra clrring. , \ ,' -4 f I a -3- I -r:t' f ,, -*2 gl,r',,t/,'=.j.1' U- ttx U lt S Ldp hi.m sd flr'rr.r t6n gpi lir phfln thirc_ohinlr qui. I, S*O l. Phdrr rk*a ehlnh quy. (iii s& sE lA erlc phin tliuc *a glx) - i.,; L rrr '' 9t (x) == '2* ."-45+2le '' + * r t2-2 tSphS.n tl,.r'rc cfia rnAt bi6rr.r. Ta sE n6i ri.ng ' Ez (rd= ?s T+ :y-u f y- phtn thirc g(*) ld chiirir qui. ndu tbng c.{c tich phln thirc a(rl,... r,r) li e hlnh t1ui, R6 r*.ng cira chc hg s6 ei cr:ra n6 v
I .|a' . 2. Cqro riBrr ph0h rh&c chinh quI F)ua vC,o c{c bi6n duong m.6i .r1,...,rn nhtr rau ,.+ UIE SU ' I li (m zi.: i= 1,....n. I * I. ckrllk.."rioo ' g(c1,...,r1) ' TF' -------8r, k:1 !r) Khi d6 h&m sd g(2t,...,2o.\ tr:& thirnlr him s6 ' ii phin thirc chinh tIui, t(rc ll n .Y. n (r(r1....rn) : .X " ., i {5) gi= F oigctr=0 vdi mgi i=l,...,n.Tinhehf,t ,. i-t T n*I lr
.t .1.. rnin gz @) (1) = giz = 2n s nl- ,r)0 fi -- tr. (Iik eg 7 0, i = l.-.,, n ta c6 min gs (r, y).: gS (1, f): ? * ? * 1 = 5. k*- I m n '= llltl I rCi.- tt ii ulk { cr..,,?1k... ,rank !.. Tim pgc titu tria phsn thuc k:t k:l \ .nn mlng n cf k, n .i.l'u lk .,. n a .r'r'k Bnk 'tt G.ui - *ffiYo *,:,_J k+l k:l " k=r 'i " k:l ii /i s^ 1; : mnl tren,miBn rlO,y)0 *- n clk ,QI n = Ii I ... .i.Q, fl clk, Cld thA thd1, riing k=l k:tK ilnl/l\ D6t : II cfk |a bii I --;*--F ,r+l k=t E li I\ lr4t /l=0'ra .,1 l\ xdt toan sarr: 'l'iur , t._r I ^* '!f 'Ilt 1.r. : rnin lZ1* Zs + ... + Zm) 1,n* I (.4')=o vdi rang bu6c k=I ^" \ . t Zt)}t,..., Zn>A 6 do d6 phin thue g (e', y) iA chinh qui. Vi r q1-. \ ,?' /3'... zl,* = 5 '' (io) -r tlieo dinh l.v 2 tlng dr;ng vdo trii tua.n ndv bb dA 2 lihi n = rrr; nl .F_l = i; Tl + r;a,gii rr'i l, 'hhi itrt ta c6 p F*T: ' ming(,,ir) =g11,' l):l* E +- Tt*... * T- "i ci * ... * c-. '' ;ultt 1t"1. A' = Chu .f riug dr.ra r.Ao ilang lh[r.e (g). la rhdy Y>o : c{c sd 4i,,.., ura x{c ilinh niirr tr6n tii6a rnfr* ri.ng 4. Cho.3 vtrng trdn t&nr A, t), t: rcri bfn kinh bu6c'(10). Do cl6 r-6i r1 ) 0,..., ro ) 0 tt3,: ! a, b, c tuorig trng, tiing dl6i nrdt tielp xirc ngodi tac6 ' vdi nh4u. Xct A .tBC r,A lriy chung rrrinir r&ng '9 (s1,.'. +o): : rrs-.}Y. =- I ch- .,'l ..,rts, A\ z/ B\ li=1 \I:lcots't*) ,' . B{t diag thrtc n*.rjcing b{t *eo,gz (+) core2 (+i v
,. ;lheo sri r:csiri trong A.tlitl c6 rilirin: riiiu lrinir bir't} rlinh-lj hiur ta 4" Db hibu k-r- hon trOn ,. o rnoi cAc ban giii mi1' bii tip rarr i1{1'" .cos..l =-.-(u? * toz - uz) . ?{rrr\ 1. Chung'nrinir'ring ciic plran thuc sau dr11' lir Tu tl,i el6 dilng str.\' r'a .or? *1 - Po chinh qui : 2 uu.t t?r' n 1 t . i i, t .. I k-t 1,.. _l; ili / IttL) -{ \ lrr' {t*o t U-oi *\^/ { --= ri vi thd tg' 2l J : *._ I b) g{c, y)'ii *g)o ! P0 il Ly lu'arr lu.rnrl rrr ir cif . t)r:;,,,.,., = r ,f i .u*d1 . i. 1.,;ng 6,1 -r.; .) (r. ,f E\ (!t' .zl ( lg-I--,: ,5 i-l-,-*--\-'tb i-r j=i \'lPO\ltt)t: n Dod6 \'! aj= ry:- I o I | \ , / D \ .- corg'{--!.6192{ " I i=L \ :: I \ z "! '- 'ch.ri ng minli r'f;ng c{ ' plrdn lirirc sarr da-t Ia .",*' if chinlr qui va ti,,r gi{ rri nir6 nli5t e ir:r chung 1 c,org'a {* \ ': /) 1 .l /) - rir:ln , ic bidu rt, I l.1t i I 'rr - 1' DE drrrtg liiFrrl ila lurrg ir)r:irr lhuc s (a, b,c): (u o & +.)'(+ * )ur- - r,)s(r,u):vo.,'-ur'n:11 + t;=1 i,=k +) .1,,1',o+t) Id, chinh qui. Tri t1o stry ra r'5ng . 1)'=Zl - I rlu] 5fu,"0'c)=gt1., 1, ,'-1 .\-' *'el n a)o,bro,e)"o* c)g(':,,,ln)=i:rri f " vir* lut'd.{ng thue {ll) te atrng. \i=1 I i=l Qui..vriJ- 'vn =di q:drti, b=1!1,t; d,rii, rlait (a,bi br 6f iai.6i1-1. 'I'a t:i, (c,bc) : '/{rri. bic" = *rlril :t61 .dL:(tt, D1c). Gi5. sri tlt: i ' litri do i:6 sd ngu1.on t6 pL ttb cl1 . 1,tt. J a sr.:,t'.''" 11i .111 b( i l)1, vi.r' hl i 21 hoirc ,' i 7ri. . Ndu ir1: irl tiji (er br)*'l (v0 i1")6 li6ri c ! pi thi do as : p1 r.a cd (o,c; I p1 (r'0 llt). \ri]' t! - l BAi f ll{t!. f-ho k; l, li lrni sr) i1r,iie.rr, A}1. 2. 'lhr hti ta chur'rg n'rinh r5'ng ndu a € "\ lh6a md.. rli.iu l;ittt squ :. (a,iti * I thi tirn trri "lr rlb pn-q : a' :,n , ' VuL rnni si'i tt.r: ;tlr.in rrt rtiu co {1lm*1, li : e,"rii yay v6i n -= 1 thi mgnir db Crlng lribn (tlm-l,l). Clirng rttitr!t itng ti)tt Iqi sd l(i ir,hiiri nhi€n, v0i c ) 1 ts lri.v ri't t:ip hop a s6 s*rr !: n sw cho li : 1?".1 {(a, b) hg lti(u tric cfutng ItLi - tt l.i = t,:, ..- o|. ltu trong a sd t16 khong lon nhti{ 1fit1 11 Pi1 !1 1. c6 srJ nr\o c:hia h6t ciro a'thi c6 h:ri s6 o1, r:2 L&i giai : .\1irr,,;i:r Quittl1 Ctiong, l6p i1C'f D4i {n1 } az) dA pal * q: paz - Q (rnod ai' I)o hgc 'il8n'g h':Jr I{a Noi). Ta ch*ng n'iinh bii lo:in (p, a),:1 nOn a1-az.l e" OiEn ni.y 1ih6ng th? tbng qul-i, it. Z' ,le N'(v te tnp hgp c5c ru xA-y rn, vi 1 { az {ar -{ a. .nhi€n), p lguy0u iii, (;:, q)-1 sao cho f lr€N "ii 3. Bay gio ta chirng nrinh bi.i tolin" Ta c0 (p.rr * (, Ai: {pm * r1./) tli I n € N db k= p"1' /.': p*l ko. l* p{,1o: 1c1, il nguven .Lirong im. VOi p=ll, rl:1 ta c6 bli toSn cirr' ta. to, lo € N vd. (p, ,fto ) : (P, 1o) - 1. fo d,6 1. 'l'ruric 116t la r'lru'ng rninh lXng u;ir r', (i \ : (l"t'p;'= i'' Theo {.2) I n2 Glrl .: prrz - q : /tsl6' (c,c)= I tlri {o.b) : (rt,Dr}. no (e,,1) = 1 nin tpm * q.pkr) = 1. 'l'heo (1)' 6
: lpm-q, p^l : (,r..;r*g, i'r'6) ir;tv {pnr - q,l;)=};, -o) Loi giii : lt rli,irr liign cria dl bi.i rtB rlArrg Tuong tr.r (pm*r7, l) .to. \'rly Ao =lo. lto A,)j r'lrung rninlr du&c. nOn lir ) i1, V4y A - pkr-1,1, i., l,i.*. ;r-= ;r * 11, .\ !QI" . . l) ?'rlrdnnT itct{t 1i .?.1 = I. 'i'a erl i EAi 'ElL4,1 . u, b, c, .r1, lri Isitt so duc117 llt1rr rl :i ..r'., + li 1191 /;--:T = 1,'1191 < 1 trtdn a < b < r: { rl < i. l)htrnE ninir rrln11 ud. bcl .r2: .rt + ti llg: / I -T*: Al(t+ Vol,c,i) >t(t*ri)rt(l-rb) * : 1i lle i + 1/ ilgr? .- l.1lgl2 < I I 1l{! +c) * tlu lrl}, .lih:in x6t'tlr.{3.ring ir'z nhAn gi6 tri r'0 t,i'. T'r} I.di gi*i. k)oit I'i Ba. I61; 11C'i' Da'i hric 'I'h"ng cliv kdt irt'rp.r,rii hQ thue cria dE la tri lhfir': V' 1,. .l { 1i. . n. .r'6 uhAn cAc gif tri 10 ti-. }ti IIop IIa \0i). 'Irudc h6t ta clrirn,q minh rXng di ltli s6 I 1a sri hirrr' ti" n0n ro klr6ng lhb utrgu gi{ tri " bri:rrr l,lu,-r., \'a ao ,i1, vigI gi&r bni toin ci'1 d.uong n,y th6a man'*1y--{ I t}rl qu i vF viQc xit 2l{1+ t/ Lt> 1lt1* r) -F.11(l -t- y). 2) 7'r&)nq hqp 2: x*.( t. h.hi dri (t) tr6 nGn , Thrlc. r,iy, l:it rlfing thuc..tr0n trronq diirrrrg r'ir:ll llrE llon: r'6i circ b{i rl5ng tiiti'i- siit; I )>r,)rn-i::'..,).rz ).r,1 ).r.o=0 (2) 12 * r + yXl + ",1 "*: ( 2(1* .r,)(1 -r i; ilSt'tt-: sinai, O ( at {'n12, , : 6Jr. t,irc'{1* ha-v l:.' !hirc, ci;i dF lr tr& ilrirrh: (l;* y' r;'tt *t-,otbs siirz-U+l r sirrClg + I,l I9l. roszk riAy lA bdt cling thftr riIng, dau bfrng ri.r' ra lilri +-i sillcrk+l ^ silr.rg .= Lll lUl. coszk c-yho{csy:1. . ce6-gl - ag 31at -l- 6tg Ap drlng bdt dir:g thur trdn cho i:l tl'rr$lg hsp 22 ' n : e,'g =c'(oc{br1 < 1) j t --.b, ll ; tl; : *---- coscrk (3). . .t- var=uuc,g=v -, ti(rt;b,1
sdt: tihu h6t c$c bqn.g.iri loi giii t]i Alu Nhdn nn 2 X I (irsi1 GX*ur*r1r/CB-k)= -khdng tl{t diEu-kien lihdc O .f,o .,or.9!j1_Ljl 'k,sous11/C!=k:0 khi l&m buirc c.hufEu ridp rit'(3) sang fu) fr3 n .. n "a, .c6c bq,r elBu b6 s6t trrrrrng hnp 1 lihi giai b&i. * E (uu+r'*.an-k+lllCE = (ur,* uo) E I.iCI. Ri€ng ban phing Hb |tdi (Ao t0 DHTil He Noi) k=0 l< =0 ed itB cAp t(ri trrroirg h.gp d6, nhung ctng clrua n6u $iBu phf,i chrng n.rinh irr
' .YQ1' mna SAsco * 112 khi;B'='f)'= lv: a I lz . cc sin --a-- .4:DC + l /2 .6d sin--:i- .,{'BC ( ('tr2(rre* hrl)-112. V6v .__-trong+ trudng lrop ndv nrux S-1ggp: 172 khi e'Dd : it'BQ - 1y. I .NhAn xdt rlng khr' AECi ld lu gid.c i6m thi SaFc*( t./:. Y6-r' rnax S-teco : l/2 tlqt dusc, -.. chJng ' ,- han khi ABCD ldJhinh'tuOrg c6 c4nh =1/212. . Nfidn ;rii: ll{t nhiBu bgn gi&i trudng tSp 3 ,, hing c6.rh si' dung brit rling thuc PL6l€mB vd fi '" kh$ng clri ra tlrroc lrrring lifp xll ra iISog thuc. l-j' 'r trJir.t, I: 2) I'rrong tr.r, h6ir od*'llc = l thi (xrnr lrinl: f l E&i .71141. T'im crtc. gid tri r:ia k d'A fin tei ,S.\soc = 1,2. adsi.rr-{ + 1,2 br'-i r:(.'( m6i h,imsd Lidrzt:1c f (x) i,io ,io S {{{r)} - l;.ril l < 1':.i .,ril f l/2. Dr = lf2t,u,! 4 bc)= ii2 urli.ott2i, oia trf thtyc citct r. . Y{-r' ur:rx Sasst=.U? hhi A = C ;: 1r,. . . Ldi g1i6i j +) tliFri kiQn cnn: Vi Ydi /c = 0 ta l*6n e6 ihB t:iron fix) = {J n&n tr *hi cin .xdt .t) i+ kt. --L =r n t)' .\A Yi l'(i'() l) = &. 'r'?5 r.0i t; * 0.nrin ta suv ra i:lx)rf(y) khi rr*S. Nhung hirm f li6n tg'c i\.,.r t nirl i phii lA IrAm rton di{u 3} l' i' la hinr don )tr rlr(,u tiing etr{t -+ I'> 0. J-) []iEu" liign dri: I]io lq.i, ndu k ] 0.ta eti t hb l{y. t(x) ,*'! 7;rs f ;ril: Da sd cic ban tharn 'gia-ilgn g&i ldi i{,?n gifii- rlirng, tuy 'vl'.v do khOne nhin xCt vn iintf qinlr l :
d6 trong 3'ltrn giSc ABD. BCD, C.4D, ph&i c6 1 (doan tli$ng nr\y e6 d0 elii hhfing vugt quA tarri gi6,: 16 g,',.r,. r.v I)),> tz,'1.. llai toirn clugg '/iil, - Iu rl,) rlii drrons tituo ,'ir'r ltint: r'hir nhat cfuftng rninh, tao,bdi 2 liinh v.urlng"cr.in;\. 'l idp theo, n{y d15ng D,B.I{. tk:irn g{p khfic ndj i:l1c ili'6nr da ,:ilo n&n: trong P3' Ndu n2 -_ (i t*.ndi dibnr'lrudi ci;i rlcqn $dp khric BAi 9;i4i, ?rang itl*h rrgd6s e r7pi,. I eho l965 dir clung trorig P1 vdi nrdi di?rn tuy ;' cria P3 vA thu-'i'bn sang br6c sair. dtbm. (;htrng rninh ring t* rndi drlin irong tr:) cdc rlr?n rld cho td .mot ,.on drdlg rli quu tdl . 3l 'I'a lai nrii diBm cudi t ia tlrrr,ng gd p kltc' cti cd.c di?m citn tet rit tru u? ,ti?m .ruiit phat vua durrg voi rndi {i}rn ci'ra Ps,'.. C* nhr tlr6 qui,r lrinh tri:n sd !i6t thric ir n'6t I l'. diFrrr crle Ptz. \rii tiiF:r: d'i vdi ditm diu nim Ldf giAi: l'a t'irir rrrili.gsnls 1,1,,11 v11g1rg ll,rrr fth phin b&ng nhau trong Pl. Poarr ndi. niti et'r d0 rlii Iili0ng rrrot .k {sO r so chon sau), rbi lu c*c diBm'chih v€ c6.c ducrng song sorrg vdi ctic cnnlr q,,,i /f ii df rlni cirr ,i,r,.,rrg rI:i,c, trinh vudng 'Lini, -vLri,ng ,IBCD. cria hinh vu6ug. I{6t Iui, dii. cho ctugc chia. tbinh /
j \ .\ #ti -'' .-_-f,o;^_*'*'--'' r €,48'= r{r' = B'D''.- BD, luc gi6c ph8,og rlng ., .,,** -? vdi tlrdng ctr6o BD' IA rlEu o AB' = B'C : AC. , ', '''--=__/"'\ TrI:e16 ouv ra l AB'=A'B; A.l)': A'D: At::BDg ,r'i YAy hirrlr hOp lh6a rriAn tlb bii lA htnh hQp chtr ,r'' ,.'' *' /T" \ n1idl . Goi t'-* AB; u =-AD',: =.{,1'tu A.'D= BD = A'Il ta c6 .rZ"-r UZ : ltz 1 .2 : ,2 + *2 ' i "l.;;' l-*-"i*l ! \'-"..' -i't-- " \i {+ .r = g : z. Trdn: laj hinh hOp th6a m6.n r'Ou 1, ciu cfin dA bii li Iilr]h lQ p plttr'ong. i | '',-' \i t i N hdn xil I l)a sd cAc ltri gi.ii gfti toi ida soan li. ducrm dir. Ban l.dm 1'ittq Giang (llCf, pnan Ch{u Trinh. t)n Nhrg) c6 lcri giii trit hon ci. E, E[c bigt,] ctl:r{t uhi}u ban, thjirrr chl hqc & c6c ldp chu5.€n toiin, di t6 ra riSm kfrGng eh{c cAe ' k-i6n tlrr?i vE cir ingt phing uong ioug, ,r,b dgdng thang vA nrht ph:rng. soug song khi chung minh Iuc gi{e phing. 1'.Y.1' BAi 5/'I44t. Cirung ruirrh rirrrg dibu ki(n ciin vi dfi itl A .l lJl {liu li c,rr,1 * r,osBt t.oS(.. sind * sin 8-i-sini. = 3cotg:1*olgllcotgC. ii11u!1An 1'dn ,l4du Bni 5i I44. Ctro'tr, b i! 2 sir thr.rc.r.n'& li s6 i tu lhi6n b{t li.j,-. C}rri,ng rnj,nh r.*.ng ta lu6n c6 E*i l-/i44. 'i'im ba chir s6 khic nhau ;r, 17' : I ( c o sft b.co sa - e os,|t u. co"st,)/icost, * "o.o) r( i L, - f Sao clio ihn11 .iia ldt ci cjrc sd ba eht s6 too bilio rrcrr bibu ri c 6 vrq t.iri .O r,rJ,,lrnn .D' I/, r'it..- l+rr gdP iru Iin si c6 ba eht s6 tgo- .tlr Kh.nng ir&i .r'. . Bdi 7 /144. ? rong driting lr.dn. dung 2 dA-r. f1'-'1u1;En'\'ur?n HuY cung AB vi. CD e{t nliau tai it{. eua diUm gita Bii 2/ tr"i ()!rrrrc r:inh llng: S r:ira -BD, dLrng (irrrlng thing SllI e{t AC & ff. a,) CO r'0 it;lt: irli b; sd nguy€n duong 117; tt' F ei:1ng r:rinir r"&rg n[lIic = AMzlctrz. : stro clio ,) DA Hbng Anh lln l * Iti "" t! -- P * t' La BAi 8i Ia4. c9; R1, .tz, fis, Ita ti cf.c bdrn l;) trihi;ng cl; .c6 3 s6 rtgrrltir d.rrcng ill, rlr I lilnlr crirr cAe rnitI rIrr dluong ung t.oi cric tlinli lir,o ih6t nrin \ A, R, C, Di cia tti diQu ABCD rrgoai tirip mdt .:t fili; *- fll Il *-I) .,2 nrirl chu cd bfin.iiinh r cho [nt6r:. I{Ev x6c dinh 'fr6 Buc 'l'ltot tu.diQn riB t&ag i?1 * lts + 1tB + fia'cd'gi6. trg Ei; 3, i4i1 {.lrr: "r , r; li ai i si thr;e. 'l':rrr gi6 nh6 nhfit. tr! lirn rrlr.ri,:iri t ;t'r illic 7'a I'rin lqr. ., !-r - | ryl '+- l:, I/i 'l-"irtt + 1l+ Iuv -- { $di I 144. '1 1.1111g kL0rie giln rhn .1000 diErir sao eho kh6rg cr; 4 rliErn ndo ttbng pirring. Chung YiJ i l).U'f -t 'i !, )). minh rirrg cil th'b tao n6n 1000 t6 cli0n c6 rlinh Dda Phi iJiin.q " li cSc di'6rqdh elio vi. Ith0ng e6 clibm chung. ts6 Bd lih6i r'os! - ros/icosl'ii i- I] llg= J.'=i';lt"",tl' EAi 10/344. Cho tam gi6e ABC c6.? = 60o, ccs-fu cos{Ir * 1} -- Ggi o"r, vi Fl irin irrt:t lI r:fc .sd hq.lg l$n hrrn ll : 7ia, A^B: 1. l-tai iliEm ehuytn dr)ng .r.dng 0 r'ri nh6 hrrn 0 trorrg ri';,. til.'ttz. '.., tt!. .quanh tlreo ilrrcrng ehu vi cfia tanr giAc r-6.i vAn : t6e b&ng nhau. l)ibrn xuflt phAt,tri: x di theo . 1) {,hrtng rrriri} r'irrx c;,, } Fo V.,' ^ 2l Chirng ritiuh rirs", tbit ttii ,n*lim an/iJr lir tirn hu6ng ddn d, rliEm .xuflt ph6t tu.B di theo llrdng r ddn-e. HXy tinh kho6ng cich' cuc tiBu giira hai - 'dilm t rong su61 qul trinh cli rrl ?n d0ng. giiri |;xn 45, lfgugd Y1 rrrtn Mda '41
Tffi$ {e*#w ffi## $xw** ws&i rm&m r#p rs s*ew uu#r v& cwsm s$r sffiv*ru *ss{ sr* pry rk roAH &ffisfl rH'ls#s r.,$; tr,* r E:n,{.i: -"t . i I. Tr{r cEsN IIOC SiNfi Cr6[ TOaN $ai 6. i{0{ liin}r ch6p tdnr gihc O. ,{Br_ eo rliQn r,{r*. tz. ToAN eudc lges tii:h dril' A#t bing S. 't'inh thb rir:ir crja. hinh etr6p, bi6t.rirn;; rn5i dr:,ring cao theo thu'tu ha Cudi lhAng 2 ridur f'$SS tiO girio dLrc cli 16 chuc Iii thi,'hr.rrr lr1,: s.i rrh gi6i tonn lrlp ll tolu qudc. til cic ai?m a. B, r.' lih6ng' bC hon r.ung iinli c0ng cria ha.i canlr btn thuQ*.m{t d6i di(n ioi Theo thrrring li, rn,'ii tinh rliroi. cir n:dt d0i cAc clinh rli,, tuybn gdm 5 hcr: sinh tirar:r du, Cfle khdr eiruy6n tof,n crin h:ti irrdng.d+i hoc '16ng hqp't{A NOi li. dtai -hoc Su pharn l{a Nd,i i ,,nng drroi: cri 'Iheo.thrdng l{, e6c gili tiiusng gbrn gili cA ddi tuv&n ttrarn gia. .&fQt drli: rli"trrr .eiia r-:i1c rloi tu.vEn d[r tlri u{rn rrtl li so iror: sir,lr rlang hoc ntr&n vi. gifri dbng ddi. Nhiing rl0i tuytn rna sd . ,i. 16p 11 atuoc r:heu tlOng hcrl. a'i1 alOi tuttn tinh, iuong hoc sirh khbng dti 5 ugurii'thi khdng dugc ad hge sinh top 11 chiEnr rr0n 5C%. tlry-xet gi&i tlong doi., l. Db rhi A. difri ed nhdn .ir&ng sd: 29 giai). Gtdi hhiit Ngul'6n 'ii6n I)ung, 'l'rucrng,'tlai . ^Db ihi gbnr ti bai totn. Iirn ir.rrng hti rrgr).r:.' l'I5i 'iSng hup IIa :-4i ilrlp 11,i. lroc rrgny lirn lia. bAi rrong Ltrdi gian tSO Ir"friit. . Tdt c[. bti lirrr cria hoc sinh drn+ uii:rn phorrg ngay cudi n6i bubi thi v:1 giri t.6 lt6 Giio rlui tidi ;ifti. dE cti{rn. 1. Ir$rn 'l'ring (liring, truirng I)h::n i-ihiu Trinh, a Nam Di NiuE (i6p 11). N Sdy I hi t htt nh,il { l5-2- ISRS'. Qu&ng -l'hnnh 2. Dinh Ph6.p. tr-rrong Phan ChSu Tr.inh, Bni I. 'lirn trir ci cfe g+p so ngul,dn (:r, g) Quirng liirm Dn lilng (Ldp 11).. . th6a mirn phrrong tr.inlr .rr. - gr = lrrr * B,- Bni 2. Cr.ri M li tf,p hqp td.t.:i, citc hirm sd Gidi ba. x{g djnh vOi ingi sr5 ngu,,.&n vi irhaiur, *hiing gii/ i.;iui-ntr l\lintr Vir,r.irucrng Cl.ru Ydn Arr, H, tri thrc, th6a mln cic tinh chil sau dfllr, : iiQi (lop.11t. (t) Vfri' rrri:ri sd ng,.rr 6n .r o,,r ri t,hi 2. CtrE Qrrang Qulrn tl irdrg Long -i'lir'rnh, D0ng l'[a i' . {ltt. f Q): /( r' * y) +;( r U). .i. \'.i, (liri IIorri l)r'rc. trrr,inii li IIblrg Pbong, (2) . /(rt14 11. ' thruh ph6 IIt, chi r{inh. 'fim t,!t r:a ci'rt.hdm s6/6tI sao tttrt ftl e;i/2 ,1"'Irang LArn 'IlIsg, truong Ld IJbng Phong, ' thiinh ph6 11.6 Chi l{inh. Bdi 3: Mol lrinh htrp ch& nhit viii t,'i.n tt,r,i* a. b, c bi r:frt LrJi m0t m{t piri'rrg
( i !r ;i. Vuong V{n Ilrrring, phr., I|6no , HAI tim nr0t s6 tlir,rc nAm bgn t.Ai tliv con chrr.r,€n to6,n, IIAi Hung {. N_gu3-6n .{nli figt, trrong Chu y{ri lrlr' .r3....irzk+1.. ; 1d nlm bon phii dIj, con { .An, HE N6: lf.2' .,4'...,.r er,..t ciln ddy s6 ni.y. 5. Pha n Dat Plrte. I.0 ilbng I,ht,ng. g. Cho tain gi.ht. AEC can &.1. \lE lhirih prh6 Hd Chi.ti-1*n; . Bai tia .{* Minh 9ao cho g6c cia .tam rlign .{lJCr l{ bing 6. \igu1,6n Quing Crrdng. ti.u,t;:g clai lrr.,r. !a thau. Oibrn ,S chav lrdn A.r,. tim. gur: tich tlm 1$;1g hop It.\ \Si dudng lrdn nOi 111':p 'tam ginc .S/.?C. 7. \'6 Tharih IIdng, rr.triinC i_i Iiing phjng, l thdnh ph6 IIii Chi .\linh Bei E. Hrrinlr \'€n'lhiinlr, lr*riug Ngu-c6n Vr,rn -- fl6rg .3. Torr tai irrr kirdng nr0t tam giAc AgC tird.i th6a rniin,liai dibu i;itn : pirii rih/:ni fioi rr; 'sin2.{ ,. J1iii, Iha Trang, 9. Phan Qudc't'hanir, lrurir:g l_am Son, ,l hanh * sir:,B, - .si,,zl,'= coig^,1 -Fcutg}i * cotgC (l) I I6a :i> un *"(1, - c)2' (f l i0. Ngu1,6ii Fiij Anh'Ngu1.0n, tir&ng Dus Xu._v6n, .. trong d6 ,-r, 6, c. lir cic carrh t,rrong ung rldi ciiCn vcri c{c gde' A. R, ,. r,f, S li dien ticf; trm Quing 5ar;r [)r .''i rrg. 11.'N*urUr, Iih{nlr an, li:rrling gi6i: ABC ?. eudc hoc tirrd, Binh lr.i 'l lrii.rr . 5r;ri? llti ihir ltai I2. DoAn An IIfli. tlrrong l)iran Bdi.rllrArr,..\glri tai 4. (.lrn da gif,c li)i n canh Tinh. Ar,tz.,. .r{n n6i llip. ironl rltrirrrg tron lftrn O l_i:rn kirrlr /i vA tfim 13. L0 'Iriln li;i. tr.rirrng j.lrii phi,-1n, iiii (J rr&nr trorig da giAc ni-r. N6j tlinL ,4 1 v6i cfrc Fhdrng dinlr rdn lai c.fra da giic ta duo,c .rn:l) tanr 1-tr. ?rln l)u-v LIir:h,'i.,r.ryrri)Ir 'l,r.rrng gi*r: 414g4e. .{i:6S,,t+,..' lt.4n-t.1n r1a c6r: b{n Vrr,r;rg. r)u-r. Nhon. \ghia itirrtr lrinlr duirng trdrr r:Oi tiep tuung ,ng: te rt, 15. NgUy0n IIinh Tudn, rrrrlrng -I'hiri 12.": " i)iiidn, f t-2' lliri Ph,tng. Lirung ti;. min[r r;ltrg: {gO,l]1ang I{u1', rrudng rJni troc Su p}ram *2 HilNdit. n .- X ri { /?{ncosftln) .* n * l). B. Giei d6ns dOi {tbng sd: t} gi[.i) i=l Gidr nhdl : Doi tu.vlir Qriing \;rm -. lln \-JEg Bdi 5. 'l'irn a db phuong trirrh Girii nii i t-( :' th:1nh ph6 Ilb {lhi, }Iinh (a -* 3.r2 * eos(grl:) .r.r/s GiAi ba . ( 'ti:rjrn!r plr,J gn -a'r:0 Ndi. tr€n doan -- t ; [b] c6 nr0t sd l6 nghigm 'l'ntirng dai hoc 16ng irgp i{tr N6; Gidi klaug(n l;hich r Do.i tu_r.Frr cria tii,: tinlr Bdi 6 Gi& sfr f I*, rasi liAm sd trtn ilurlng _. lh,'iog tliuc sa() Llro vsi rnoi sd Ilrr.rc.r: Sirih * lri - l-iiicn, Ilr,ri Iirnq- ;l.l,rnh *fOa, Xgi,f f inh r,r1 ciia trrrrlng dai lloc :,r phqnr tln Ndi [\l \.1 ;) ] -r. 1.. ,,,!lr.'ilg rlrilh riing / co r Cr sd .diBrn khQn6 lien lt!r:. II :TfiI Clt{rrN n$r .ruv&H Qil6t il[A 2. Flan ir s,ic.h dgi ru.r i\n lroo slnh V!4t Na,r, dp Dq ?'#r.t.CIAN c?u*C rE rse3s etQc tbt reArl qu6e rd l&a th{r 26 tpi Honxanhky ; Sltr lii tlri ,'h,.rn lrr.rr's.; 1,1, 1;:i',i lr;in !r.ip ll Io;.rrr PL&n Lan, n$m L9g5 [udc. Itd giSo Jir t,i r.lrrrr i]r1 1,,.r.p,r t.lr,- ir d,.ri tlr.r,. (sip ri';1i ti:err llrir ru rl iF,n tur.bn clion) )oc sinh di riir thi toiin rlr6c ti lii; thu 2tj tai l* liguvtlr; a- Iiin l)ilug. lhs'n Lan cltti iflt ri;:lrii:tg hot,.:inii d,i doai _ 1up ltC l, I)ri; 66. lDrrg hup, Hrr \i,i. iil.i .c,r ntrnn (giJi chinh rirrc , ,i uii, i r_J,,]'re- [bich) tr.ring trr;i6 rlu6r,. Nhirng hri,, sinli n.ir. ? - LArrr Tring (iiarrg, Ioi: ll C'1., .Irrruns pl, l I{ Flrlrn (lh;iu 'l t.inlr UA 'i\ir:g,. [troc I4p tlrrng trri t]d \iri ,rd li.r:r li:\i llri tuyFn hai fong ui _rrgl_r. rrrdi ngi.r lnrnr.3 bai r6dn trLng - 3*-'t{uj'oh {liru i{!rrh Yir, iap ll CT, trrrdng pITII Iin.\rr. IIA Ie,i_ p+nr I80 l)litt. 56 lrrong ri,ii tur.0ri ir\ ii ngu:ri. 4 -- O11 Oul i{liiiuh^ Ir-rp l1C,f, Trrrorig pl..l,H Ir. oe ru \gu1-in Y[n lr6i. N.ha 'l'rnng, , , I NSoy tiriliri ntrtir C.ho dn5' sci tlruc.r.;, - 5-*- i{u}rih VEn. 'Ihnnh, ldp 1lCT, Truorig ;8..-t I r2.....,rn.., drroc ITTTFI itigu1,6n VEu ?rAi, Nhli i.o,,g. Fc atinh theo q' ui lrrA I : t ,: ,- - -.CIr0 QqalC Qui'6n, l6p 12, fr,,rO,,s- PTTH 6 F i = z'S: 'un+l = VB *rn/V.,.l - l, n = !,2,i,,.., I I I r3 t. t- iI I i. I-
Lich s{i To&n hoe WH ETJ vrfrc GHAE F*ITT#NG TREtrFi ffi&E n,# ilA !'\H '.5V DIIUO\G triuh dni sd bfic n ltr ph.rrong trinh Pliuong.trinlr ll) c6 2 lr,in. n0il rii. ngi-:rgnr I c6 dang: cria phrrong liinlt (3i tlr:oe x:r.- linL 1::' d.u 't vilo a"oo + o!.,D-1 +'... I on*10 *rrr=0,ao*0. rliiSu kiQn ii Strtr'f p=0 ha-r'ri.i = ---!-' 1'1t i16 Edi r"6i chc pi-rrtong, trinh dqi s6 bAc nhdt vi b&c 2, viQc gi&i chirog 116 rlrrgc irinh bty rdt xAc ilinh rt, u ta giii hQ 2 phtro.rrq lr'l'rrlr 2 i;rin: k! trong chrrong trinh to[n hqc pirb thdng. C6 J rrrr = -p13. diBu rl6ng chri j' lii, p6c c6eh gi&i ciic phirong ltu"-l-r''" =-'-r' 'r trinh'niy ngrrdi Babilon cSeh d$y khoing 4000 n'5.m d['bi6t m{"c thi khi d6 irgudi Babilou cltua b Ilu hQ n:i1'. ddng dirh i1i l.it!t tar rii il':'gili bi6t dirrg clq liy hiQu bing chir nhu ta hi$n nay. plnron t trinh bric h:ri : mi phiri di6n il4t bSng lOi, phfri rrriir tdi gifra , thg hj, 17, nh
r I t t t I i ..t I I -:r=Vnq2+!{;+t,tzt- lrir, ohin, chia, nAng ltn Iir-v thrrt r'{ phdp ctrug, I ' khai r{n, trlL: lti kh0ng giii duoc phrrr.r"ng trinh +\t-q2 _ ttif l* * t,*,,,; bir S lbng qrrit b$ng irhrrcrng phflp clai sd. Rflt lidc irong cAcn chirng :ninl: cria Ruf ini .ou phg* zz = Pt'i -ql': t 1,,7a l'i,e12r n s*i lilrn vA plrii il6n nir nr l.q?4 rrlrA toAn hoc A- Ben ti8{12 -* 1S?9) ngudi \au.r- rrrui ctrurrg rninh . 'r oz\l *q!r * i o{,_E': :-: 'lifil lufln cfir: P,ubini iu61' r:6ch ch:it rh€. l,{6t vf,n zB = P,ii' -q 2 rtl q! : + di tr6.r. ra 's*u d6 t{ ng}ri0n e ti'u li}ri' ndng Ap 1,:J 2; -Y dr.rng phuong' phep dai sd r"ao giSi ctie phuong :, _ 3t trinlr clai s6 bAc eno lron 5 dang tbng quft. VB pri/_S z - tt,t 1O r- p3 l:; vfin d0 ni-r'. nhii"toAn iroe (laloa (1S11 * 1832) i d6 Pt, p2, p3-l* cac tllr bi,:3 tirn sri I cu th'0: ngutii Pir*rp b&ng phuong phiip dlc bigt efia rni.nh di r:l-rr'rn.g nrinh drrcrc r&ng : 11161. plruor:g ilinh dai s6.bAc ltin htrn 4 itlng qrrAt dEii khdng gi&i Sau khi Jri6t , r::ir;h gi6i phrrunq trinh brr c.1. ttuoc iring p,hrrong ph{rp dq,i sri ,,'ii r:6ng b6 r,'i.o ngtroi ia lai '3i tirn cdch gilii irirtit-';'tg tiirrh bic n1m 1830. C6ng ti'inh nAy cira Gato': phii g[n {. Vinh drr tinr r:r r:irch giii phrrolg triir.ii i:itr: 60 nIm slLi iilri':0ng i.rd vri nlrcr nhd toIn hgc { thuSc vE Pirrrri i' n}rrt cl:i s6 l;g..rdi Y r.ii li .ru{t clrtn; li [iooe L)[ng i-jdt.qiAi lhirli iai, hoc tro cfia t.lrcil:ri:i.'. Iihoing i)roi giair sau kii; loii ngiroi miri hibL; drrnc, Phutrng pLAp r:iia liin la circlr giii irhir rrno iiilir i;r'.r'3 (tiriii Ir\ Ga Loa dirr:g i'ai tro qriau ti:o rrg r r)o srr phirt nArn 1515) cl€jrr ii.i:i cdng liri circh gifii phrtng iriEri r:f:ri rn0n.dai s.i r,'i r11c i:iil Ii. l.i' tir'ur'6i trinh bAc 4 ninr lr15 kl,r&og ;10 nlrn hho.ilag nlli.trir. th
theo urQt trinh tu c&n tlridt. tOi tinh dfl3,v{ ngai 1Ap tirc ghi lai r:i.o rnQt rrriuh gif,;. con. Sau.nAy (aAf: lan itii tung tlugi; doc ho6c tlrr,ri, oglie IiB clii cri rlet r;h& troitg l{rrr- biog dt'r l{ ciin pirii v vE,i.ri lich ciia m6t sd phAt'minn ki srll, lai mA thot B. d.igu trong Iich sir kirt.:r hoc. nlrri r i{,. \irr I'ou lrrn NhA torin hoc t,h6$ Iianri Pofingr:ai6 mdt ra tlfnh luAl van vtt'tripdir: hr.r. v gr nhil lrr..i!t,,, lfln dir phAi ili nsir lrong tA rn tiang 'bin kho[n Acsirnet tinr r* 1ne d&y e fi? n:rr'rc.... Niiung ca.: cia-v drt vi lihfing t*i'nAo giii r:bi'rl0t plrrong hg'n cd brFt ri.ng, r6 ni:iing .;rlrit. riiirrh r i dai trinh. 'l'Oi gIn si'nq" 6ng nru.thii-\' nrinh dang di duoc hoin thi'nh tronq nhirng,,iir mcy hiiv qi&ng bAi ,,,,Itlr sirih vi0n. i'ir gifi.i ru0t c{c{t tii,i !' , tr6.r" lre'rr har,{ Irhrrorrg'irinh ait pi,ii gJc l+i {' kh0ng ? Que khd rirr r-uir 1oi c6 iir+t nrSt tr.*.rrr phln llim I trrrri,'ii.iri di nqir. Poarrge:r16 tinh rl0r vir du gt,i lai idi ,gi&i cira piruong tlinir do. _ -\ird LAe hoc Nua [)irrri{r'i 1lerr.Jdr0,. *. !r rrnq lri:: , tinh trlo ill kh$ng,thB n]o di6n tA nbi l)Eeg bl;g v lih& toAn lro,: nbi ti6ng Kallo Fhrichdri:h tu&ng cria minh vl hg. tuiin fuo:in citr.. c6.r: n6uy€a Ge"iro trong rni;t gid.c nro d:-L gi&i drrg: trii te{n t6. Ilrit liin, saLr klti lirn vigr ciing ilrirng r.A li6n nri.6ag dit phii v+t l$n .r-rii no trong sudt 19 tr.tc kh0ng nghi ngoi, 0rg thitip ili, o*, if ong rriv 'rrIn: llOi I 6ng dE ahin th{,v iliBu di lirn cho t&a t}ng tr&, Cdn r:ac brn ? Uhfln thluh cirfie e$r: b6n cing thirih bAt tfr. (lhinh .\lenddl€ev kE vi si.r lii{n eu tlur:c .r:hirrig gif,.e uro k\, diQu nhu vir,v..! 116 nliu gau : .( lrong rna iOi nhi.n ihiiv tirn lrn,ng rni. iy d6_ cie nguyOn t6 dLrr.r,: uep Ait iit'tAc IlIlit-l &effiffi **gx ri[s r]x THrr 6n {u${ Tr$r firlr r0lr . frffi&s ffi#ffie {t{ [16l? " rt lfrr Tntlx€ fiAtr r?Bf r i{'iflp lri*','; 'Flig.rn Trong DIng Sun (11A. pi,I'H Eitn BAn 1 Chi Minh); Phgrn \7an TInJ;* (L-y lB, cao ding Qu&ng Nam.Eir Nirng) :. Ngu,r 6r, l,rir4 iiirrh Vie n, sr pham lhinh phd IJb Chi Minh): plrrn Thanh Pham ilfl'u Trung(tril Cl'r,ri nli pI'Tti .i-hii phi0rr D[ N&ng).; e lrtiu 1!{inlr 'tr'ri, fr}n Xiu't;-: Lhin. 116. . llinir, Ngul'6n. Khfrrih ,4.n vir Trdn thi \gOe Bich (l1u'I vi i2C'l'. Pl'Til eutlc Hoc liuti, Ijinh Tri Du.y I{h{nh. ir.d fri. i{rrj"ntr l,'itr ThAnir. Ngurin 'l'hiCn) ; 'Ia Ei.nh '.[lLirrg r.ir 'l'r.hn FlrLng (10CT v:i Minh .'{g1q (10 Cl' vir ilCi' p"f l.H N,guyOn ian i2C f , p1'1'H Ng6 Si Li0n, F{n Bf c) ; Ngyyi,n Viin Tr6i Nhu 'ilang) ;, [-B Thi]u Thanh, tIAr" H,:,,g Quydt (10CT. LC llbng Pirong, Narn Dinh) Du Dinh' [,f Ydn ]'Linh. Nsu-viu Dric Ngrr-i,in, Ngr,_r..:il Ydn ?oin (UE, irl"l'll \guyeu lluC, Hi ; So; Ngoc I{trrs (118, ljB, ilCe, ii(j pti,llAri Njr$n I llinh); NguvI,n ttiii'n Anh tir['1", p'lrrir pnrrn. BQi Ngltia Binli) i f'{r1-1,1;,, iSri 't'Lr1g. Ngd 'l'h,:nh Srrn, Chiu, Ngh+ 'Iinlr); l{gu_i.6n thi I.an IIrr:ns (fOlr. Dinh . VIn I)iing, Ui-ri:g eurir: .Al:i i iit), j:- l-'1, l{ 'P i f lI I'hir 'l'iriia I-orrs An) : 'i'rhn liinh I{h;1nh Quang 'I'ruu.{. Qui Nhon N.ghia }inh} i 1{ciiir.g .l'hach. I J Cl',,t'}'i fI{ Long Xuvin }-6 'Bl 'l'Lrri;rg {li l-uorig 3 Ngoc Phrir:, i.i iihirirrr i lllla'r,r 10,.\1 i,l I li Yiin i'ii. l,r.rng XLr,i,6n) : \gu_rI,n \':in 'i trrrrin (128,, 'lriln Qudr: 'f irtin.'Qrrirrr.q. )iqrr r. Ngi:i:r IJiair r Flr*rir 'l)f'ffi t,rru Yin Liit,.'Virh t,1pg. rlii,rr Long)t '['iri !lintr 'f&.ur { l1A.r P I'l'l{ l]ulr 'ljnh i : -.1'i'In llri -yqirrtr Tirir-v 'l-i0n.(11(,'l', i']'il{ 11}rg 1lh{p; Hinh); L4 Du,v iICG l-,IiH iioii ',;i,ori f , l,ehirr St l)Ee Diriu. 't'tra1;/ I )igu-ri,n Ngoc fhAi" (12{i. - a Binhh Ngrt-v6lr {fur'irrit }iilio {g l,.p:l'CT eu,v Nirrrn. l) I l'il" 116 CA-r.,. lJ{n 'l're) ; . Ng1r.r.6n '}lirrh 'Ii4rr Nghi.r 13inh) I 'I'r':in l.iu1, iiiriii (ifC pf l.li 'i.r.rrne (118, PI'll{ IIan'I'An 'l hu*n Hii}; Phanr (tlii Vrrr,rnq. Qu.r' \lrorr \g'lri:r .i.;i:rlr): I'ir:r,rr 'iir,ln ]'iri0n (11A, Fl"iII -\g0 Qu_vEu). .)Snc.Nri); fi6 I Ngon i I lP. f I'"i'li eurilg 'l',"riu.i,' ei:-r. ijhi::: Ngh;a Ngq;r- Minh (lht1u (1U.\. ITITII Pleii:u I, Gi* I-ai * Binh t.;' liguy6n (]ia Ilirrr, 'l'rarig. t-,1 rn Blng U l{Ji- {ion Turrr); lIir N6Jr-rc P}rrch (7}I, .p it)S 'l'rrin ir;.rtg .vA 12{i l', l' t I lt i.e Il,ini; Phorrg 1:11r1}1 1yl1ri i Ii', i,iinh, Nam t)inh); .Ngu-v6t {loring Long,(ltil2, Clri Itinlr) \l{rrttln i'h:lirrr L,... .r*gr:-vi,r itoiiiig P'l'-f tI \gu):6n l{ui, 1'ur i'lrla. Phrli Ii}rtnh) : \;1u1cn I'ihAni l{gu_v6n Y[n lla ql2,\s vi lIP. p l'J';l Ngu1,6n 'l'r'ong Il;ro (118, P't tl1 ;\n Kir0, (iia I.ni Kr,n 'l'hrr