i5)
Chii n&n !n iriiiri r:ri iliBu ki(n
(CI)
ar ,-. .-a: ) tt.
1. 'Irong nhilrr s6 cia br{o Tr:{5 iruc vA 'i rrbi
tr6, c{c tran. <19c dfl drrnc gitli thi{tr vE tfu:h v&
hrt6ng r'ir* hai ve*tt:r. lli'r il\ lnsl hArn sE thrrr''
',:fr4 hii vtttcr, tuydn ttrr:1i rA dldi rri'ng' cirn goi
In m$t deng rong tuydn ttntr dl6i xr'rng' Ctr 1ti"'
i{ r'i,ti }rai veet{t tty ! r. 9, ngtrrrilr ri;t; tirrrnil
ung m$t sd thr'" kf "hifu l:'r (r,g) r":'; dttrre gQi
li fir}1 rA hw&ng, vivi cle iinh chflt sal dtr''
iluq* th6a mfrn, vg! moi vreirl {. S, , vi) nroi sl'
thge a:
++++
*
LI {,{ } ?+'llrirr+rtile, -q
r - - 4'+
i.1.. r.: rE d y + l].f lt? + tf .: ), {i,
(.r, Y +- zi - {r:,4) *. {e" r)
\r * z, gi : ("r, U) + (:, y)
toi,it : [", o]l * "ti ii
ir\
(r)
{
t
i3)
Vr'ri ti::ii-iC huuu$ "i r'rr: g';' li'iit.iii)' rr6lr*i
i,,, ,ti"i-' u*r.1ia dtl '!r:,, 6d' ' ;t xii-r'" dirng- irintr
f'r,r,'' o.i,t lilria t'-iin t' i:i 1*li1 pir'li'r ir'rili dl.ri i:ii
1'4et o.
tli,
I,
1'' :, 6ri5Cr .1; J ri:.) - t
?;!1.1 !i+('J51 .?
t,*
tr.oiig rlii a ia 96,: e rig hai vei;ta i..i":*
'int'
ci8 ria.,rg vi iir{-t ring neu "2: 1 v' := !' (tt' u} = 8'
ihi ta c[ag r:o:
+++$
,i.2 - t, ;iZ .;- l, irr', p'i = U
:, !]? i:i dlrrrre ri ngirie lrinir hoc cria tich vd
hrrrlng, l* r:l l quv rilic rang ndtr.u. r' lA hri vec-
to ilrr;.: vi ttr?c i* I * lu J = 1) vr) t'u6ng ,6c ut)t
nltari tiri t
i.- riit = r, G,*r) = s,lt- ti,it=r
SB chung minir r&ng quv rrdc nhu trBn co
hiQu lrlt vri mt;i rr$pt*v1cto clon r i vii6ng g'ir,
ta triy lfil' th&m lhli ft' ,tr'i'li-rp 'r'i ';a vudng gdc
vdri nii$.n, '1iir di diing th'i1' r':1ng ihintr l):
r!i'
^,
Qri v6r, rt:gi i:ii[i YFtli] kli{ri' rr' p i:t} lhl 1r!Aii
++
.,'
f,
t irro E, e :
lich
i
|
-?'-
r
U '
fo
I \'r
i
!i'
i-A
"*
nh*'ra---I*-*''
'i:J'l
'?P
y=A*t+yap
*{irrl t
' I/lnl I
v& kbi dd:
+*+'*
(*, y) t* lrru l- ,e, f le * Ezul
4+
i",yl = rrtrr (u u) + {., iYt "'l'
e-ar7l) {u,.;'i -i
rt$'a i r,. ,' I
lt*r gi,i, t* hl1 'lait htti ve ctu ifrv -t i ii f'
ehr:o vetto UE, *i a, cr)ng hu*ng v':ri t;' idir
vr*to dryt ", ,rj$ vudnq gde v0l u' Gao cho gSe
tfis b*i v.{'lo $, r bBnS * r/?
{{ )
ll're:
(3: ry, ,, r1f;1o * istgt { rtyl)& "{ }}U?i
t
,' \,i, r:!.,urrrr* ditr, 'r-x;1, ll:r 'l:'' ';'i' ti'i r;'"'i
,,u*,"g .uui ru5 *i 'fii .rriflg tlu'rt' ri': riirrh nirr l'
iir i'iia
,1i,,",,oi* git tt; titr ni' rril*l';rt "i"
klr0ng r-i tili0r:g ild'ng pht''ring si' l.r' {":u llA tt ndu
ta clel tru6c c{c gili iri :
i, - ti, oi = o)>r), tu, r.,) * (p,,i) '- t',
t."
I
la co:
4
FnF
?-B
rd (g), ir{i), {11} ta suy ra:
Ilo do
lr.. Ul - l:ria 1 .rzu, ri lE + glol
lr.ql= (.r'taz - r,ryr) [u. r]
l;:;l = ittyz - rssl) 5
;,, l; ,;i
g '= ig leosa ' u f- lr7 isina ' u
_--
+:*
4
.
(r" g),= [r I . ly l*oae
il2
)
"l'l:ti ta dtii yriyi ticlr ngoAi e tia hai vect,: trong
miit phing, chi eln cho giA tri Df 0 bfia n,lr
t'oi hai verlr: chon tri1, y, kh6c khOng v& l
tlr
$frn6 th{re {r0n clro ta .{' nghin Linh hoc cira
tinh v0 huilng Vi ctng chinh tl&ng ttr*c fl1",
nsuoc lai, cd tht ISy lilrn tIlnh nghil cho g6c
hinh hge ct cr'ra hli veeto (t{rri ciin hei lia).
4F&
€
f4
Ciing theo (7), diBu liiQn r.in -.a dri cho lrai
i'ecto llh6c htr0ng x, v lrrong gric r.iyi nhau ia:
l,!,it 11n,, chit crr lrAn eria lleh rr,1r,ii ti:
_*I)ibu kien eiin vi rfti cho.hai rr,lo
g $$ Anng phuong v6i nhrrr l,i":
.
-
lr,9J=c
*>+
(r, Y)=ii
llpnh dB tr€n suy la d€i d*rig tri (l:t).
6. Bi.v gid d& co tlrr*r' -i, nghi* hinh hqrr:, i:r
qui *ac rsng I = *l l
--& ..*
{. Rr}}'gi$ niu giCri ttritri vri h,,n,1t.rr mdt harn
+,i tu_rtn tintr Llrie riia..l vct.to-lri.r i, l.lrOng tldi
x*ng nhrr tich r'0 hudng, rni lai ln phiin rri,nq, .
tric l[ gid tli r:iia nr_i tlBi ridu (kh0ng dbi gi:l rri
tu-r€t d0i) khi ta hoin l.! hri tecto. H.)m sd n*r,
ilrroc goi lA nr0t dqnq nga,ii ci'r.,r hrli,vect
'['hgc thd, mgi e{p uo.ioi'ri'don r.!*v:i vusng
gr.rc th.ugn cd thh phin tfch theo c{p ol', nf,"
dE ldm & trEs (?r. Vi f a ilriv r.irrg
t:; - r* I -+ 11117': :,: + I
Ycri hai vecto b,it ki ;:;r
tn chon ul cnng
(e)
huorrg vdi .rr {xern l-rinh l), thi ta cd
r:,Li
fi---
I,xi .r
IL;iI-- rL-i:'ii-,t J
tfuf ?'is Eit-ha i
Ir.... l/l = l*, egl = " tr" yl
Nhulg, klr{"e vfii tich v0 hrrong :
.+
+
.r. -_
li = 11; ji:,,r?. u i- lyl 3in&" r,
{ 10)
\'f.v:
I
'>'+
ir. Yl= * l,l, .,:l
li
F>,t+
i;''; = l'liiii uiu "
i.r', 3l =t g
(u)
'l-ich ngoiil dinh ughia nbu tr€n, cr)n goi lt ti'elt
lfcfi, holc tith tharl ddu.
Di: ln j nghia hinh llf Ef,f [r, gl. ]',duclii Jri]-
giii trr tuyQt ddi, thi [:r:" yl ]rfrL&1firr tirh cira
hiah biuh hinh i'€ y/ri 2 \.tei:aij ;.r", q idinr caah.
i{
5. Cfing n$15*i tich r u huong, ta h[1. ehon
hai vecto u! p nilo ttu. khAc khring vit khdng
d$ng phucrng. T5t nhi*n:
/j
I
ilil=0, lilfi=,r,
Cdn [u, ul, ta d{t
*..,
*,--^']F
A
)t
J'
ls.**-"
o
lf'*'l = 6#rt
" =-({-l:}
ttlnh'3
Ndrr lr iluy tr-O-c r ir'rg di$n trir:h mring ti*u *
> ti vs rnang ri:l u*. n6rr (r'j-u
n€u grlc
thi iihi dr) [* qi li didri ii,:h c,i liasr,] cria liini.i
bintr hirnh.
ei tdt rrhi€n
3 Id rndlt r0 thuc khde kh6rrg, chon tu.r,i,
{:*)
Ling vOi cip lu, af. Ktri d6, hirn lr, y] li hoal
toin r{e tljnh. Qiii v&y, lri i
.r:.rln -l- rzu
y a17p * 11zu
t:r :.
7'*^',., *t
( l5)
.lr* giire 1i, h
f
il{) "
Fiai tich v6 tru6ng.vi tieh rgorli i[Eu-co'ung
dr,rng rQug rei trong hinh hoc vccto ptriing' N6i
ctrung, lilri ngrroi ta chi sei 116n,,nhitng-tinh chrit
*h,r,iibrn thirlg lrnlg, direing thing"dDng ilui'
rlu*ng thing siing so;rg' doarr ilring rhia tleo lj-
i0. r-i's"{ di{rt tir:lr" tr'tc lir nhiiug tinh ch{t gr.ri Ii
ilnh chit a fin. tiri ngudi ta cl:i chn dling ddn
tit'h ngoAi rua tlr0i' t.eir l. lri rrgtirii lu xCt ci ddrr
nhirngli,ntr cL{t r:tg li€n clriarr den dd eldl vir sd''
thi ngudi ta r:itt dring ddn tich vd hrrdngr mi
dei khi cfr n'g ndn tlrirrg.,:i tich lgorii nita'
Iirlr Id lrut';rig.
nguiri "ri
':["R&?' Yff ffifr
qAc wffiru
*nr"r
#iA
\-rJ1\-'
wffi srroffi
ilii Hs{#
ffi&
BAI 'i*A}I
ffiemG
vi qiras{; S*il
.",
Zht. 12b -i- 6r f 2c -) l/c{ iib > t/2Eb<5
o Ii = ? => c ngu-r,0n i6 bf;t lii',
e 6:li *ic=:3 ho{c e l=5.
11 6rri lai nghiQrn ciil bAi t6{t} iA:
s * 2, b*2, c E p u$u)'en t6 vA cAe ho{n vi'
trofle o =?, S=ii, c =3 r*A c{c ho{n v!.
BAi SoAn *. ?'irrr ld! cri cdc r$ tguy€n duotig
[1 lli L,urn iL)li rr. ' i:ri. cli,' iran g[;; iil;3rru !l triritrtg
flL
i.,ai tt:, n 11::| r.r': r r i'i: iu th.rt', Sir, it''rrt; lir;
binir llirig vrl,i tlhalt, nghla iA n0ri l-ir t! ao
d&i e {ac r du tri il,l, ciio nl::iu t}ri irir6ng larl
tlra.v dbi irili tual. i'.hiing hqn ':ia'; bni to{l:
('l'im t5t c& . ci.ic sli ngrr.r,,0n t6 a, i, c srio clto
rdD. ital li aT'inr irietd ngrr-f€n
obc.{o}*[r:''i-
rluonS Jr .{, : s;lt, clio .}S: = 1} i :: *U * : D'"
lir nhirng btli irtxn ('o linii t'hi: v*a trBu.
l. f6nr l*i. trong'irinh lror: prhing, v#i hai
telto tirv ]' r. I/, ta l'cAc t1 !nh tioh r0 hrrdng r'd
tich r;4oni lA:
G}= l.lJA r "r , J
1... ,;1.- lr I ir;t sin s l
vS lr: hsi biiltr llrt'tc 1r&ri, Itl stir
-*t
,1. l,l)" -tl lr" g l' =. u' . !t'
l)irrX tl'rri. ni-i'r:hr: ih.{r'qLl a$
r, ll. : \iio cl?o 19: =9
-f ,j + u + :,
DE girii nlrti'ng l.rl}i lnin dang n.hrr tlrd cd thh
cd nl'lil:rr cAch Llrfrr.: nhau, tt\y ihuQc'vAo trlng
bii ct-i thb."l'rong biii bAo *hi1 rr&-r't6i nrudh
gi,ri thi$rr r 6i e&r: brrn ni{rt phurrr; phAp giii
cAu lr&i tol{li !l'&i!,
i. Ci ba sd brlng I : kh0ng lhrir irti r': pl:u,rt-lg
lltuh.
f a-v
1-
g -. - :: Iei1,; i- l1 * a: rt) lr
?. rli.
:', ,)> S.)'1, : -: l'"*ry '' iU * .r - I
t)(!, -. 11. rri r - lb y- l. l6n e' -
ii=(.r'-
= 11, g - I *- I vir-:r; :"::12. g = 2, .'= l.
1a>y),)>j.
Eet u =a,-'j, u = ll ^3. a. . : * 2
Giii : llo :r', lJ, -- tharn gia vlo I::ii IoAn binh
tling vrli nhau n0n. lil:0rrg nirt tini.r tbng qirAt
t:i gi; thidr r'> g ) , ) ] l'a ed cic .kiri rrflng
snlt :
+ a> u) ,u ) 0 "r'e ta c6:
li'i rr f o * rr' = (rr + 2)(u +2)(u; * !1 =
'It bist r*ng, n*rl ,:lt'] tr'sfr .llrr.re 6i.. "2,:. (ia'
lhi bao girS i* i:i.rng ro tii& srip clrung lheo !!rr'r
tu i,5r:g d.dr hog,e gi6.rrr ditrri. Clir 'rrflrr e$tt * 1.
u2,..., #o ti,r* gis lirr.-r nrc! lr*i lr-rirn iriuir r.lfing
116i uhnu, thi l;at: gic' ta'eirng cri tlrh gi6ri bAi
to6ri vdi gi& tili{r i,; t( a: { I < an }io[r: a1>'
a?pt..Pan
'Trtr6r: i'rdt ts'gili i,li ira; lrlfln I'ttn niu ri tlan'
Bii toirl 1. f inr irli , ri ctlc sd rrgogdn {r} a. i;. c ,lgo tho abr, {. ib.;- l,t + r t.
J oru, * 2(,ap ,i- u,y .t- g,u) * 4(rr a u *_ru) f I
Suy ra : 7:u.utli-2(uo*'ulu*uru)+ 3(u-1-u*rrr) (*)
-
ta >0 thi v6 phli cria (*) ldn hsn hoic
N€u
b&ag 16, n&n ding th&c {') khdng xA1' ra. !r{6u
r,i ia ls.i xtl 2
rr,=0tr'7-2uu*3(a+p)
tludng hqp:
Suy ra cb r' iri' * c,r { 3&c.
NEu ap$*$br(ale
lri
Giti: Yi eAc sG a, b, 'e binh ili'rng r'6i nhau
nen khOug rn{t tinh t"bng'qu5t ta Si{ tbi6t
e(e(c.
0 = 0 =* '7 ='$u kh0ng th} xi.v ra,
u } 0 + u-? *bI + ?r{ol-l(u*p) }E : vd
'|cb i lle -ica(oeb,
mAu tbu$.n v6i lidi ra. V*y a = ? ( ri e ngulBn
t'1). Do dd :
T6rn lai nghi0nl ciia pirrrorrg irinh la:
'J', -" tz, u -- z, : - I \ lt eac fto;r l) \ i.
Bii
toAn 3. Iim t2 s$ ngtulin Liw,tr;,1 . ,i,j,)
Giii:
cho tbng crie e/rrin.g &dng llrlr cria clrin17.
lt thAl rfing { ed rltli' ni,il lihrrt ;rlrau
at, oz, dg, q4 thanr gi.a vao bii loArr i'inh iliing
v6i nhau, nGn':khCng niSl tinl: tbng rpril, tri gili
il,i6!
,?ri 2'
n0n
(r)
t
at)ar)rg>"ue
Ta gii i phuong llinh
1r1
(?)
.r1J2... rl2:.1'l *::z -'f .. +.1112
.'1
il
\\
hay
'I'rI (ll w" *1r2... ;12 ( 12r1
t2... r:tz --( tZ
ri
li h i rlo li6 ( li trrcrr-rg i!rong vl!i :
i (ol *d2).r2 .{n1 -os).rr3-t (cr1 -44}.rr= } (u)
J lrr- o2t.tt+ {oz'-os)r3f (u2 - o4).r'+ = I (b)
) (at ,r;l),r'l-r(/rZ -ol).r'z'rt,tc-u4) x4: I (,') '-'
rl iot- ua).ri'i(n2-o-l).l.e*(ar -era),rs* I (tl)
Tu hii ('l). tl,Lre hii'i, 0ic"r,lr(,p tinh (ai -- (b) I
(l;) -'(,'): (c) - 1,ir ',, illyua i:0 irr,rrrg rittr"nq:
(3)
Vi 2a-= 16 > 12 nen lu i:)) ra rhdy trolrg il
s6 ca, .ls!...,.r1a iitrOng thA cei lron 3 s6 lorr
hcln 1. YSv trong t2 st1..r'1,.r'2..... .1rt* khOng thb
cd hon 4 sd l6n hrrl i. Do d
l. 11 = tZ = ... = tl2 :-:: L izhOng ihdra rnin
t
,r*r2tfvrrr+:0(tt)
phuvng trinh (2).
2' *i )sz:.1rS:
*
... = r.l2: I, t& i2) rilrt' r,t:
c1 : l1 * ct."| 1l = 0 ngn ohriDg ktrong tht th6a
rnf; n (2).
Gi&i: Gt:i cAc s6 phiri tim li xl. ir,z,...
Rd ring :rt, a'?....,.tta trinh d&ng r.6i rrh.au
la gi6 thi{t c-t} rz...2 t,p}
f (rt '- a2] {
.r'l t- r'2 - .1 3 !' ,r'tr) = it
\
- o;1ii--.", *.JZ 1 .!tl
ji4; = tl
),u,
I (r:a *'id:r - r'i *.r': - :r.:+ L,l ti : lr
[ {rrt - d4}.r I -f (,rz '- *4i 13 * ia3 - i:4i ,t 3 : I
(
I - ct -'- 1'? + rg 'i' ;r4 = 0 ($')
i -iol -12-'.t't+er4 : s (c')
I (or*uu).ri'i-(uz*er) re+(nr*aa) .rs = I (d')
L{y (a'} + {c') d,}qc e,1 = rr; (a') * (6') auqe
.rl s ss * .t4 sur ra rca = 0 ([') * (c'] adrpc
,l + .tS = r4 sttt rtr x2 E f,A
lha.v .rg::: rr3 = 0 v;r: pl:rrong tri.h {u'-) .r}'
"n
i. nr> EA> {ts: rurt: ".. : .,,l1 = i, suy ra:
Elaz: 10 { ;e1 * 12 €} (tr -* t) {*2 - l) : 11 : 1l.l
:.e2- I +.r! * I : ll,. :l:t*i : i' \ri 13-. l)
Tlt d6 su' r!
xl=#4..!{at-e4) zt:12. :7."Z:2 r'A rS: 'f4 - ... =..zlZ = l.
4. :Ub tz)
kh6ng th6a mln vi rs ) L
5. t,tb.L-7>.rB2. u2
(2) su.v ra rlrzns:rae 8 * -rt * 12 f rS * rl
tr'Ar vr'vi o1 )> ,12 ): a3 ) aa thi nghi{lr tira h6 id :
.r? =.Tlr'= ii" r'I =.r4 = |l{at *,i*')
Cliir r' riing n$r. (ti. ltz. r]S, tl.1 c{r rtr,it lltri ltr
khAt' 1hi nglrignr ring cd rntit tht'r iu trrrrpg 1i11g,
Ching han ,*,, a2 ) a4 ) nt )ns
tl ) ri = ...-rlz:
l. irt (2]
suJi ra &ieLx-t: I * .rt * rr * ct.
'ltrel bAi loAn 2. la c(r .t 1 = 12, ra = 2. .r'r : r :
D{t tlt: .r 1 * },
{!.lt.r2) lrJz*2i (Us- 2} t g++2t
=, tri * g(gr * yz +"43 * ya)*...
h"r
Suv ra
rs:...-= r'r* * l. 'I'r'r
(4)
!12: *z - 2, r7g = rB -. ?.
!4as4* 2, su1' .r^ yrb 0 Vi = I. X.3. '[ r:,r tar
e15 {1) ttrong ri rir7ng 1'{.-i
l6*yr*ilz rus+ lli: thi: .rl = 1:4 ,::0 r,A rA - rS = llteZ - uS.)
'f r'€n day, la ile rlt nrdt sd LrAi to.{.r vE giii
ohLrong lrini;. Ii*v gio ta xet m0t sd .bii loi n
iogi khite.
0=711il I llz *,t3 * u+) * ...
!j1= !]2 = y3 : y4 = 0 -> :rl = t2 = t3 =;rtE2
llri6t rAng olc)>
T6m iqi cAe sd etrn t im lA
.rB =.r4 =.tS =... = X"1g ,. I
15 E .r'6 :
I
Bei to$rn 5. {ldc sd dtong a, b. c /hdo mdn
di'6u kiQtr gi, d? odi mqi sd ttt rthii:t n. cde sd
oE, &4, c: ld dd dr)i ed,c cqnh cfia m$t la'n gltic?
6lii:' Khlrng indt tl*h thfrl lhng quA:. ta gi&
:- f* = 2:
... =..r,ll
-
t) Fi6r"r t)>b)2 c -)> 0 llii I -)$ia )tla Yr c|t
s0 hta. citr d0u nhir- hsu I nln l6rr lai sd trt
nhiirn n rli lOn sart eiro- (bio)o +'(c,'n)o'{ t khi'
at6 ,n + co {.i no r*n \'ui n i!qi, rru. Iro, .ro khf;ng
phLi i;i 3 raoh ciia ir;di i*;rr gil,.c.
fil = I3. 12:2,
ho{o
,1'I:.1 2=.l'B
2i 5sri ,.r : b>r-')r0
\. i vg1' di&u ui4n chn tirn c&a a, i, c l{ hai
e6 l,in nhst phii b&ng nlrarr.
8Ai toan 4. C}o a1, a!, a$, d4 ld, 4 sc) t/rgc
rldi nt.ot khac nhau. Gttii t* phunng trinh tctr:
I
\ lrr - aalrg*-lor - oelrs +lor - arl re = I
llrr. a1l 11 -5 !o, - nrlrs .i- loa - d.lr{ = I ,,,
) Iaa - a1l.r1 * log - ael rz + iaa * otlcl = l "'
i lal - oil.rr * lnt azl..z + la+* asl13 = !
thi oh = b*>',")-t1
ltii nroi n st1 {r nhiEn. vir r5 rilng rhrirg ia tl6
di i 3 canh cria rn$t t$rn giic.
['
\ral 5012 d 5. *st,., ra :r2:{ li 10 (dpcni)
Bii tonn B. ilho i ,,1 f ,iuc l;lztic nhnu a. b
Bdl to6n 6" qhu.*t rninh ldrr.g lranrr i dotln
th&.ng,m6i dsan edtlp dai t iiai, unr I ( I <. 13.
cti fhl chpn ra 3 ilogn db, iitm ..1 c*nh cit,-t *;6r
lr:n gi&r. Ch/rn1S t6 ,r&ng bdi iorin Fhdng diin,;
ndu ci\i eling 6 daan th&.ag.
Gi&i: C&r sd a, f, c, d ir r1A1' cd lai tlir irinh
d.
d&ng n6n ta gii ttridt a < b
'l'a nir dung tiuh chAt tlen db girii bli trr$n 6'
(iiri s& ? doan ill chr: cr.r dg dni tu'o*g ung lir
It. Is. . 17. Kh6ng' rust iinh, chSt tbng quAl ta
gi& thi6t
t.=Ir{lz.+{...{il{ffi
i{iiu liiri::rg qlitn ra drrar 3 do4n niio lArn 3
r:+nlr cria mil t:rnr gia-c t lri :
Irt} t2+ t3} l II=3,
ts>:t.l-tz'za i{ I -i:
itlt ts + tA>:i + 3 = i'; ia-P ia 'i I5 .i> 3 * r. =' :i,
i?',> it 4- k,2 5 * I =- :il.
iJliiu rrd-r, rnlu thuin ltii gii thidt 17 <( 13,
biiu chi dring 6 dogn th&ng thi bii lo6n lih0rrg
ding, vi du l{5' 6 tloan c6 dd dni tLrorrg irng ll)
ll *,, lz*. 1, ls : 2, Ia = lJl 15:5, Iu =8.
'i' a'c 6 Y 1
Xrlt rr(.r., u. :, t)*(.u-:)2 *(q-t)z =(r*v)3"i
r (s - --)z n"r-- -,r' * (t -.r')s + ir'---)a * (y-1;e.
iriBu tlritc nAy binh ding r16i voi .r, u, :, I ren
no le hing -sr5 v& bfrng tbng binb phuong t'it ci eric
hiiu tronq i sd o. b, c, t!: t.ho nOn n(.t', y.:, ti*
(,.*:)a iiy-.r)2: k (khing rlbi)
ha.r' n(r,37, --, t)-i- {x2+yz +;2 * t? ) -2(t':1yt,\:k"
ga e,2 * !!z + :2 + f2 = uz + bz * cz :'rJZ a6n
gia tri cria n(;', lJ,:, l) plru thuoc tin gii tri
, 'ia :u: * yl . Ojitri t/ = r;*yl
phr.1 thir$c lao
si1 phin elria thinh eStr ciip cira I s6; a, b, c, t{.
Ii5 rang chi c6 3 u{ch sau l
. V t: ob * cil, V2:1, * bd, F3 = ad :- bc. '
* I' e=tr & * er1 * ne'- bd={ ii - c )( a - d i} Fr
V2*Ir3=r;c 4 btl *url *f,r=(n-&){.e-d)}0
*Ai to6n 7. Ritt.dngnf "{ ui+ a!+ alt ,1?6= r
Qtr*ng nrinh rri-n.q, otd lrt nhd nhdt t&a lni * d.i)a
t/ ( I -,!.1 .if l kh,)r1g 11rV uust qua 1:|tt.
YAy lrr ) t'z ) Ye.
Cho n6n n(,r, y,:' 1) chi nhin 3 gii tri hhle
Giii : xnong nrdt tinh tbpg qu{t, ta giii thidt
nhau.
\
lar - utl = .1, f ir rltrg
(oi * ni)z =' 12
lihi d
r'(.t, tJ,:. l) nhin gia {ri lon nhdt khi
1' = cz * gtl rririrn gii iri l6u nlrdt. mir Y lon
nirat Ii \'t = ub - t't ,
'
tiilrg nt -: ,rz {... -( ,,;
'l'a ki' hi{u
nritt
t./_
t:\r_i'Ji\D
tnjn
t*r.l?=J\a
t z-
: -J-
: .'
hAi loAn hibn nhi6n rlung) r'r:i I = 1, 3, 3, 4.
I'a suy ra ot+l - oib.u ) 0 (vi ri€u rEO thi
'fa c$ ia;* ei) = iaj - trj*r) * (ai-r -apz)+
tt d6
r, tj. tlib,a rhric rr-( r. y z, i):(r*y)2*(g-:)2+
tnZ nkan-bdc r,hip.r gtd tri
*{;-/)2+(l-r)z
"a
khdt nhau, n1a cae bitn s6,u, g' :. t biin tlti€n
ttd ld hodn ui eie cac so- a. D, c. d? |'di gii trt
rrdo cfia:rr g, --, I iht n n,rlirt gid tri 1dn r:1rrii.
nhd nh?it? Gi&i: D6 chung minh tlnh ehdt siru dA3,: ndrr
circ se, duong ei, b, c t}r6a nrEn a) b); c tlt\
chirng Ii d0 dni 3 canh eria tarn gi6c khi ta chi
khi a.1b+c.
I
1
r
I
.thu ng
viri 7)i. +...+(ar+i*oi))(l.-i)r
sltr ra lr:* a')?'?{j * t)z.rZ Liy ibng cE hai v6 ltrto i, 7 ta co
cho
nIILt
Xhi d6: t. = d, ::=6, ! = c, I = d;
ho4c rr= cr : = d, I = t, l-- b;
I = c:
ho{c o = if, i = b, A:d,
hoEc r : d, z=t,
ll= o" i= b;
h6ie e =lr, i =(I, iJ 6 C, I sd;'
lroire r:= c, : =rl, Y s Il' I -c;
!1 =d, f :=c;
ho[c.znb,z-at
I=d.
ho|.cr:=d,z =c, ll=6,
.l'6in lai cd E hoAn vi khe.e nhau lim
n(.a, g,,:, l) dqt git tri l6n nh:it; Y6i git tr!
nhf,t,.'xCt luong iu.
Cu6i erlng xin gfti tdi cic bqn mSt s6 b&i to&n
(j * l)z = iit :i;2 .. (j - t)2 xo = *2.L
'sau d6y :
i=l
1
:
J.
9. a) Tim e(e s6 nguy"6n duong *,!, z Ito eho
E
r:(r( j(5
\'^ X
** Y * zzl1z
t;
:g- 1I a1)'(i
r*l
b) i rrrr r'il c sfi ttgu_r i:ri ilrrtrtg .f , i/, ;' I lxr)
cho .ra il 1 .:' i / ..r'I:i,
{ l..3.irB :} :i
10. St sd Jlrcrng.r':,.rJ,.T5 tho* rtrl.ri..
va rl * eg't- .r:g "i i/rr-i" l'':r'3 "i Lr.r6
12. ChIrng nrinh r*ng, tl'r 25 sr) dLrarlg iihic
nlilLr cri th& r:hrin le hai sd, sa+ ctro c*e sd cdn
l*i ir iiring thh bing thng ho{e hif u t:ria irsi -sd
r tl'r, r'iroti.
i.;c iior: I
.< li: i iili:
:ni n .ro-:
:3. r.lrrn'g r:rrrrh lrrr', ri:ing lltut: sarr:
l,;i -. uil{ui * egl ."' (at *rr;}*(oz- qiiidt * d3).."
. {,r;'-ir5,}'{- .,. *iug*- *1)(*t,*d:) ... ius-u+)} 0
'i'rong rto ol,.nz, .."" o5, li c*c sii lhui:.b5t ki'
Chlrng ;r:inir rir n{:
voi nroii:1,t,3
a) ri*i
l-l)'l'rong 3 so rt,.rz, .r:.T to tI trng i r0
ll.;r) \'oi g;a iii ugrt-r'0ti nau tiia
lai e{e s,i ngtt;.6ti ri,irrrt3 r.,; -' ll.rir
-r yl + --3 = iasrr^-.
L,,.
4.'
1!
1(rtt+^''}.niil-.t)+r)
iA sd ngu".,,** io,'
r * il;;, r r:ri E -- s11k
x.ri.\,.'
H ffi&ffi
{ysmi.*
[&
ta#y
j;i f iru tlorig iuiitr s6, dirr titn r&i .:i t,irt bE
L;a i;ij suo cho thng cAc irinh plirrrltg i'ris "lrirng
ehia hdt eho lictr cfia ct:Lirg.
Sei 2 l3'il. Iiu"r o;ir
,'6e Etiu t.liri"s r '+- i; "r
rnd.n .phtro n5q lrtnit.
?
'2 ,r, 1 -' 3,Z 12
tri idn fli#i pd nhi nh?i!
t. btdt rfi.na .r'. S, : tJrda
I'inr sS tr njli,;r: n nho.'rhfil *u+
1,'' - Y: "'
cho tltEt p/:rl* cd eilil d{t!t ld l*i *rrf * :
il(n198*+ 19li{ n-i3); riilic*+ +' ii} 1 r: * i ir...
'" i 198{r' {nlptl+ + l9'\ I n '$ l$8ti)'
ryi !'i+i)
+ :zl + g.na
L#i siiti :
ti{&i Yinh, l&4, Pi"l'H ',l'*y sr-rr,
tsl i' tlz i-:? o lci- lt't'21? * 212 -r ?'yz
--t
.;r' 1 *1ffi
Bil l/l:|9.
iuong dironu vdi
++(:i, -r g + z)z + {o'*:)z -t (.r * giZ =:
tt6i vli-r' (r -i- g -l :is {l vi dtai gi8 iri
(r i-g+:J2m2 khi **: = 0 rA .r'-r; =0.
Yr.ry * , S + ., i:6 gia tli l0n nbdt l;, /:
(A. ,r19st * ltrilln 1-ll) e i
Ltri giii : Ci,c pirtn si di 11..,, ci rirr r;g :
ti (n138a + 198.1a * I' : i.]
:,t i- - i;;f'r.
Cie ph:ln *6 dr1 ii ltli g:1n i.hr r * r:l:l klri :
(1i, ntgsl - t9E{r } & . l) a ;
.r .. U - .- -
-- -i'
I ;ii;
- _l -t
Ftk8n xet; l{t ci cac lqi giir gL?i sE dtsu
dung.
li.Q.1'
tt,i
r,,'-f :: vi c$ gia tri nhr., nhii ta
It6i $,'139; {l}rri"ng rtti,rr r,,illj-I*no IiBC
giuo 4il*'; rli* t/rrring pid* 6idc A&lI ptti t{rtsng
tru*c iitiir .!firl$ sont tr*; r{lr. r,d ede d.i?n litp
"r'r-ie e*i; ,irirrxg trrirr rqii fiip &..tSr. utzi i* olt
-'1 {. ri,im frdr: rr.:r rtrdng !hino
Ltii gini; i:ri:r !&rr 't'ring tiiang, t1(.;'tr, trhan
4'1,1u '! rinh. fla NEng. 'i a phAa th&nh : truong
Ir r.I trl :
r, t;5 I,lg8{,
'Ia rlli*n ilii.r ng:r-r' firtg' '-'li; fi* { iiii ni9SS --
198 ln * j= tSE:, la s$ rrgir-r'r'i, ltl rdrr I i . ,:t.t \. i
V I = 1,19li4. \-'i1rr viiv gi{ tri ft... I lim e ho cri,:
phAr sd tl[ elrt l& l#i gi&Lm vir hcrrl eirs do I lrt
rd ti: nhi*n mlrii nhfit tloug t{p sd; irr nli!*ri n&n
n-1 ehinh li gi& tIi c** rirn"
Fthtrn xot I i,ii. t,';ir i,.r,, V i i:ia, fi6.ng Vil ir"c
(1i Cl', CIfi'i'H tii !tl.,i): ir{, l)rrv XtrAntr (11 f,'i'"
lrgul,dn 1'*n 't'r11i, \'h*'l :'*rrg-i, L.{rir l'ung 6i:ira"
,\gu.v6n l{b .{.rih irigu.vlr:. 'i.r& e t tu&n, hglu.t iri
['lrlng Snr: (1: C'f! Fhan Ch*u 'i'r"iril;, Ea lirirgr;
HBi Virih {lilA,'l'li-y Son* Iid Xa;i}; NSuvin i.i;.r:rr
\.ii,'i r[* {)ut' tiini.l {ili;. i2{i 'l lrrng Vu,,r:8. Ut:r
Nircrx) t* Pirtr;g ,\ul,n l,*i: (ff i,1', l,aor.!*n.
Thanh il6a) cil 'l{ri gili t(,t. B4n Ngrir,{n Yarr
Quaug {1lc'l', l."ir rr; Scu. 'l'h*nh H*a.! rr'un e trirng
rninh du{rc rtriEu lihirng dinh n-rgah hon : ( n = I
Ilr s{l tr.r nlii*n ahfr nhst i*rri €.h$ *r phin td rru
li tdi u r&;. :
li Phirn gi&rr r:ria 6 r:*t d*6ng irur$ bilh
trd5 tei i) ngt:fti dcqn M:\. S+i f lA lAln dlu'trn64
tr*u n$i tiip, il r'* B lar e*,-' rfilm ti6p rrit crla
?'
-*
r.a Op//d..
/
Dlng th-ai do d" I BC, ar,lCt vi dc_Ld6 n6n
$11-y I'a ANtiiia. €Ailldr
'G'ci if lA. gia.e d.ilnr .:fia t{e r.l dr. Iet hei
tain gi6e "trlf viL aitrlr ta ta{y.
duong tr6n n$i ti€p roi iC yi
"1g. Kh, d6
JL I tc, /x -L a3. ,r'a
c6 : ,il]? = ifr = .ffi
&+ Iff) = R,CIZ. Vrir rlrp,rlc yuA*tg_ lai f -"i-fi,f
gi*c IttDC noi ridp. iI'* r.IS nfiC = JfC =
={fi.-Fr')ilft)
- AA,lfX + !)H;MN = IiBl0N,
DE''MN
EK!lltO tdo EK nixn tr0n dr)
KDil*ll (da tiD ndm tr6n d*)
Suy ra$xff
.A*
fiBE *E OMN (2)
KDI6M t
KilF = oMP * hxnr*t:.o.liP (3)
Ta c&ng i.:i A$ = 1s *tjffi = [i +"'6 i , ,r,
(1) vi {t) ctro r;r thdr oui:triN. viv D. r{,
Il th9ng hir:g.
'l) IlrBm cit D ninr ti.ons,loan iI&;
'\n.-
suy la F{llptl. l{4. de 1{ fuang thi-ng di qr,ra
F ri song song v6i OF n0n suv r.r .Fl( nim
ir€n dc. BiEu niy chr'rng t6 d r, dy, dc rtbng
qui.{dpern)
HT
4'
-\
\
til
Ta ctng *6 t*rrr
gile EBC vutlng
gdc t4 i lL 4I H r,){.
It
I ri gil:c rrrl;
ii6ir, Tu
116
EHI] E! Ci, 1.
(a 4 c; i2=a.gK
ltay D, l't , K,
thdng hdrg.
Cdch 2: {erla lVguyEn ltuu Iodr, Jy'guyEn Holt
Vfi, l0A ud 11 B Trung }'-aong Qay Nhon, Ldm
'ting Glang. 1|CT Ph,ta L.hu Trinh Di .\&ng).
N&6rr x4t. Ban T,r.*r.r An- Vj*t, ttcl.. phan
Brli.ChSu, Ngh6 ?inh cri loi gi&i t6t. NhiEu irAi
xdt thi{lu tr'*}ng hop. DIc bi{i hai lran phan
-Phuong"Eat, 8I{, PTCS'I'rung yunng, ijs N6i \.a
D5 Thenh Ssn, 8A, PTCS Bd Van Dan, I-ie N6i
cd gi,i tr.ri giSi;
t
N.Q.T.
Gqi O, G, Q lin lu9-t la tlm riuring tldn n6i
ti6p A3-BC,-troos tAm A*llp vA diBm gi&ri eira
,\'P. Da thd-r Q la auh crja'if qua phep 1,! tu tAm
G, ti s6 (-
:). oorg thoi do Q nlm rron da
\ 2i
t,b, dri iOM (r,i etng vudng gdc vdi 5fl) nln
suv ra .ds chinh te lnh cria dudng thing OM
qua pliep ii (tr vr}a ntu. HoAn toi.n tuong tg ta
cirng cd dl vA dc lhn luert lt inh cia c6c
dudng th&ng ON vi OP qua phep vi tg t{m
G ti s.i l- tlzl. &{t e{c rluong thEng OrV, ON
OF dbng qu.v le.i O n6n suy re cdc ilud,ng thEng
ds, db, ds ciing dbng qui t4i O'*inh cfra O qua
ph6p vi tu tAm G ti sd (-1l2) (dpem)U
BiLi 4ltS9. Cho A rSC. (,pi lt..V, F tri cdc
t!U! qilrn e*.a drdng tritt nt)t ti|p u6t cric cqnh
BC, CA,- dB. Gi{i sri: riu /d cl*o'ng lhrigg qwa rtttm
11itra e&a PN ud uudng g|c i,oi BC, ai li ,fuar,g
thdng q*a dibm gittt cria !,]I ua uu6ng goe uo.i
C4, d, la dtong th&;zg qua tlt?nt.gitra eri,i-"y-t ud
uu6ng gdc uoi A8. Chung miuh .riing
d.6, d6, rlc
Sbng qut.
8-
i
li
';
Lrri gini: Cricft 1 (c*u Ngugi:n lib Auh.lgugcn,
1-l Phan {hduV.'rixk flrt xdng). Ggi /), E.,--F-lEn
lugt li fiiEm gi&a cria ni,€, pil vA" ilfrv D6 jtng,
ehting rninh duoc * I,fffp * Anpp.
?u dCI bnlet:: - ttf)lpr, i'i} =;tr;
(r)
Gei O Ii ti:n dutrrl trirn n{i tidp AdgC.
Khi d6:
t').v LBC. oNIa,4 vr op.l,_AR Nhgn x6t: Cde ba.,n Nguv6n Birh f'n, Trln
Quan (ICCT, 11CT Fhan ChAu Trinh, Di Niue),
Ph4m Xu*n t,ec (tt8to. Ngul'6n Ydn 'fr$i, liha
Trang), D6 ,vgoc Minh Ch&rr (10A, PTTH SeikuI,
Oia Lai * iion?um) e.tng cd l2i gi&i t6t": NhiEur
Bei 6l I'3$. ltgt tri' gide gh1nh co eac 11(te d6
rli$rr &dn.g nfura. (ltfing minh rang rdc t'qnh dd
cita t* lSiac.bd*g nhau.
bgn kh{e c6 lr'ri giili dirng nhur:g ruom ri, phuc
tap. Ban El6 Ilu-r. Khhnh (1lCT, i\gui6n Yln 'ir6i,
likr Trnug) q6 .\i irav nhuog db vQi vl nOrr J$i
gi&i lhi6u chinlr rac.
N. K.tr.
Otii: Cdci i'(cfra Dang Va \on. liCi, BHl'Il
lln r\Oi, Triin l,)u.r t-iinh. 12G. Tlung Vrrong, Quy
Nhon vd rnbt s6 ban htrAc)
Bii 5r'139. c) Iinr phu'qng trlntr b{c J cei
nghiQm ld cos (r/7), eos (3rs/7) r.i cos t5rl7).
Xdt tu gi{c ghiinh ltsL'/] c0 TI} : ;A;ut
j--
b)Tir di hda tirth I6ng I,zt:os irlT)" +: li cos (3m/z)1
r''_-\
ADC = AIlr..
-i- t.'co1 (3;!i).
i,l
^
rt
-
Lai giii : a) edch l (crja b+u La6 DuSz liS6nnr
1: fT, Ngu.r,Fn \tin.'116i, Nha 'l'rang). Ta th{y r/?'
3n 7, 5Tl7 la r:!cr nghi{rn r:ia phutnrrt trinh
3r * 4,.r: .= (24'* 1)r: (I: ngrrr'€n) n€n'cos 3r: *
1- cos 4r = ll. Mtr ta cri
Gi& sir ,{A { l.l-}' Vi 2 drrring tron ngaai ti6p.
cic tam gi6c ,l.RIl vu B'*D l:ir'g nhau (do BD
chung vi BAD::: BCll) ntrr tir' ,1 1J (CD ta su1'
ra Cl) --\ ,r;(,'. I xi tit ! ilrr.trng ti.i)n ngoai ti6p
tarn giac ACI) ,t W.l,jX-S
,:ting hing nhau
(do lC'churrg r.i lBC'= -'lDr.), tu r{D} f '; ta.
su-\! ra CD { e,g, l'6 lj. Ttrirng ttr ndrL nB >C,
ia cfing su-\' r'e rrrlu thr.riu. \a_r lO = L'D. tuong
tu ta cirng cb AD = BC.
*!=0
eos 3r: J46536 - 3cosr
cos 4r : I (? c(.)s.r * 1)2 = 8cos4c * Scc,sBr *' 1
Suy ra 8 e oe4.r'* 4 cos3.r, -'8 coszr * 3 eosr*
hay (cos r * lXB co33r * 4 cosz*-4cosr*1):=0
Nhung eos;: * I f 0 ncn cos (tl?), cos (inl7)_,
cos(6rl;)t$ 3 nghigm cfia phrtong trinh tlrs * 4yt
*4u* I =(t.
{deh 2 icrl:r nhibu ban). ila c6:
s6s (c/7) * cos (3riz) * coo {5rr7} s
- lsin (.]ri z;*.in tl +sin (4n/7)*sin(2?r.'7]*
+ sin (69,7i '-- siu (lrl;)lr:sin (rl;)
:: siD {ori7)l2sin (r'7) = 1i2
66s (rl7) . cos (3r:l;) { cos (3r:i 7). coc (5i/z) +
La,:h 2: (ciia Pharn Hai i1l2 Phan CtrAu'l'rrnh,
Dn Na"gl--
^
Durrg C81 : --11i. CDr- AD. I(hi d6 ErCllr
: 6CIl * Rr.; D rLt D0Dt =(.1)A-: ORA = BCIIr
-[ rEn caL: rlgrrng theng t]D I i (-'lJt i1{t cac rToan
(1.1, - 46, f;i - i-8, l'a suy .r:r
+,'os (5ri7)cos (::,ii =
= i'(cos (nlZ) + cos(g::/z) -F eos (sa17;z
*. *.,*z1n17) * ,,ou2 (en77; *"
"ou! 1srr771172 =
= 1/6 * (cos (:m/z) + I {- eos (6n/i) +1 + .
+ 00s.(1{}n,,i7} + 1)/.1 =
= 118 * (:l : cos ("|'ij * eos (aniZ)
- cos(snl:i) lt * * tlz
r:os {r/7)costBrrT)cos(58i7) = cos (n/Z)[costsniz) +
. * cosi?a tl)]ll:
A {-']fI = 11 t;BrB Ic. g. c) "-? lllN = llljr
-\ I-'BJI : A CNBI (c, g. c)-*) BM =.lJrN
Ilu {g}'81 la hinh binh h:lnh *=i I(lF= Sfr
i
= lcos +rii\ ^ cos.(ZriZ) + cos (B?E/?)li4 =
= (112 * rli+" = =.1/6
PI
\t
\1
j'
\A
r'
,q*4
.Vf,r' cos (n/Z), cos(3c 7), eosgnlT) la ba nghiQm
r tla plruong trinh.
13 *.rz,'f .- : .: * l,:g = rj
b) l'a co theo clirrh li V iet :
t/costelT) * l/cos(3r;1'Z) * rr'cos(5nlt) *
cos (r/i) cos(srlz) * eos(3riz)cos($ntz) *
* aos(5r/Ztcos(rlZ)
c"oa (xl7) eoc(S,!ii) e og(trn/Z)
-*(1i:)'(*r,8) = 4
,
D.B.I{
D.B,X
:AC=D[]t +.U=D.,V:El]1 ulABeCD
AD =CD1: ii8 itlpetn)
8ii 7/L 39. t:ho tam th*c blic tai
Ndu .t'o la nghipnt cira (l) tiino{Y, Gii sii
(rn,n)=1)
bl * c. ()hung minh riing rttu m, rt, k
"?.+
.
r .k ,
.,
t
i - I
. * o1l -- n
(1)
h n-v
l(rr) :
fd &a rd ngug|n dt6i rrrrt ,khric nfiau J&i
'n,r* l11(rn)|,lt'to)|, lf,(A)ll V-;'
*
, = *^,o tA ng-liQln c'irt (l) (rn n€N,
llri ta co
u'[ao( -nt, n]' * uii * rn tt)* -' *
.k-.. '
,
kr
,rot-m)k f ,ii("'nt)k-i.*
. I
T u' div srtr) i'a 06 : tt ; it. I nt,
{2)
thi pr-= P i16;
li-(' hiQu v6 trAi ,'tia I l) ix l'{r')
k^
aa.n : u
do v{1' t(n{9. l-(irr(9r
ri:
' rrk.P(.r,): ,,ki.Fi.") * P(-atrn)l = (rr.r' * m)g(r)
trong dd g(, ). la da tlrrt to-i hi s6 ngu.r'en,
Thay o: 10 iio hi thri'c ni.v, la dur;c
r 1n....)
,'ikr, = f l0a -r ,n)g i !1r\.
. Ub. -t r ing (r,k, l0ra -F ,n),+ 1 r:in p : tur. +
*"m {!). Tlrer; giii thi6t ti:i p )> 10ilt', do Yay
I < i0,'r -i- ;l { p.
\:n-r: (3) nrflu tlruin v6'i'gii thi6t p la sd ngu-v0n
Giisfr m("(A'. Xdt hanr y (.r)*(c*n) (.r- k),'l
16. Bai ioAtr tlu'trc chung urinh,.
\'Y-'11
.q. [*i gi$i. Cricfr , teiia Darg Yfr Sol, Cao Yi'
Ba, O6 Dq,r. Khith, lrlguriir: ll-,ii Vfr, f-f,nr Turig
Giang).
.Gi&.s& m{n(trtri k*m'bz.
N6u l/(mll( tt2: lf rn)l( 1/2ilf(r)l i ilz
rhi l/ t/i) - / (nri g lf (*tl -r lfrrll < r
hr:'l{l'- n) (.k + n + b)l( t
Suy ra,ltc + n +bl <1 (vi k : n) ti
''lurJrlg tu,, ta c6 lm * n * O[ ( t. Do d6,
1t - ma (ft*n*b) * (m*n*tr) < 1+ i+2' mflu
thuin. vOi (2). 'Viy (1) riung.
Cach 2 (cria ltodng'\iln nlgdn, Ngu.r'6n \{dn
firlfi } ({/J)eor{li z} cas (ttt2} cos(Ctil.
* tr- rp) (.r- n)"t * I Z
thi g (m) = (nr-a) (m* k)l't - i,2".? fu2;
f (n) * :- tlL; g (k)={,r,'- m} (*-tt} z- t'2> t/2.
cii ,.i' n,a".lll'(m)i, ll (n)1, ii(r)li < rlr.
l Xdt him bflc nh6t h (x) = r (t) - g (x) thi ,
/r (m)',= I {ni .* g (irr} -{< [ ( nt) * 1/r < 0
, rr (n) ,= f (n) * g.{n) = 1(n) + ;/2>a
A (/<) *r (k) * q''{lr)(r(l) - 1/2< o
1'u dd sr,-v ra ft (r) .6 ii nlr{t lrai nghi0rrr, tlo
v{y, ft (r) - 0 hay /(..) - g (s), nrAu thuin vui
gi& ttridt. 'l'a drr-crc dlpcni.
'Ibng qrr6t h6a bdi toAn {ci'ra e{c ban l}nug \:il
,
Son,.Cao Yi Ba, D6 Du-l' lihirnh):
Cho da thuc lt4c n : I (.r{:.rlu -l c1r";i -i- -.. + an
Chf rrg minh rlng trFu ,r o rr, "1'a..... ,ra lA n -F I
sd 1gu1,6n ddi ur$t I'hic nhru thi
n,*' lh'('")1, l/(rr)[,.'., lf (*,)ll batt2ft
CAc b4n d&u e?rung rninh cluge dua vdo cOng
Lhric nQi suv !-agr'6ngio.
,Nh$n x6t : tlo str rufit ndrr rrorig tl6 ra rhidu
dfiu tr! tu,v+t d6i, triy vd_v. tdt c& cAc l.ritn gr-i,i
bAi giii d€ri plr&t hiQl r"a rJiEu d6 r'a giii thco
c6c.phuong plrAp dn trinlr bA.v & tlon.
'Bdi 8/139. Ctto p = ou.n! u2... tru (j{;}.i) 1d
m0t $ ngullcn 1,5.. Chi'n,t. mirti rring i'hsttn:t
trinh aork * o1","-I i a2.vx*z + .. l- xg;;(r (1)
khdng ed ngfufar hftu ty.
(
:\'
'Ae*rr
Bei 9;139. Goi llt ld bon l;irth dvang trbn
ngoqt tidp tant gldtc cri ..i e anh lA 3'du*ilg trilng
li*n erta,L:lBC ; R td bdtr kinh dlrdng trdn ngaqi
tdp btgc. Ciiing rninh rdng:
"4.M,'(.\ ' , "Arfft{
: .r.lt.\
Ld* girii: (]oi ;.t.tf. t,V, {)p l.a cAc rlud.ng
truirg tu-1'dn cir:r ,* .{J}C. .\ e lr_K li -4e var ldy
.iI.tr::-lA*=,vtt ihiqh ve) ilii c6 il{N/(}, l} iri*ir
brr:ir lrirh, $u.y ra.lf{=4,U. 'I'a lai c6 APffC:
AS,Uf (e,g.c).su)' ra BE=CP. \'Ay c,,j ,l"Blfff la
iarir, gi4.c cd 3 eanh li 3'drdrng tlung trrydil cria
AaRC. Ir'r t;,, ,.h dung la co :
(
. {
',\siyff
*
-- *(
"-,lrMN - ,,r,'A.{gC
rJrr:i rr, Phurri
Hli, Ngtiy6a Binh An, 'Ir'&n Du.i HinL, U6 Du.v
KhAnh, E{ng Yir 5on, NgLr-r 6n Qti:ing Crrrrrig..,)
1r)
Ldt qiii : (cria e!rc lrr u I lln
\
e,, :
v r,u }, o
:
* cos (3,r2) /e.
;' (;t"r!) = r'
f ,r"g ) 6
I'uong trr ta r:iing c,i, BNi cos tnll) .l.ii,
CF}r'o. tr:tzl .tll|
t:{t
Val
^n 8,1f.ry -
r
t"
lit - .1.11 .ii.\ . {.1, , 4 .\
* ^l 11 1-,'-\ . {- /, t rA,,
u,..
;t, 1'{r\ ,- r.lit;-..
I.o'i giA,;
" Iri ir) *- {rr: 'Ihry .r r,A g i::}ng I ttri /'(l"r l)i=
/'(r) (lr
'l'ira-i' r1 = i tlri /(.r/.1)) = /'i ,r)
el
'I'ha.v.y=7'it) rhi I'i,rl'(,r{t)t,.. 7,1t) . l1r)
(3),
Ti)' i11.,(?). {lt} ra ,.ti i'( r) -= i tr}. [r)) ma
l,:)'>0n;rr l{Ii - t. }i,1y1 f1 rhi y(/( r)) =
'I'u drt I'lr) f(y) -
(tri a, b, e l.i 3 canh lutrng ung dinh .4, fl. L,
,- ira A,{ #r. . -l-.r
1,v =d16zt J *i2,t*i ie+ 7-+:a. .*l r
tdlnh iy harn t.nsin) ) V':fr. tr I ."r.if= Sei 10, 139: Clo hrim s6 l: @,*)-+ (9,.x.;.
t'. iubng arlrrh rting iat khd.ng dinh silu tu$nq
'!u.rng t
u) /' (i(/(#)) : y l'(rt
l,)l (r.v) :7'1r).7'(y)
ftt b +*): (lr l'(.,-.1(tr)li =,"i.r)/'(/(u))=S/(c)
= tt.v.fi,r{r})) : / (.r, yr
' V.., ulu .
- .,u "\ 0,
"> , | :ri, i ,.,,s(,{,,1} , ,. '. i; . _. t:os(I,.r,?). irlpr:m)
'\ir{n xet: Cic }ran N-q,,., i;, ,t1., .Arr!) \'cu.}.€rr
ll:tC'f, I'hrrn Ch*u 'l'rinh, ita ltHng) Xgrr.O,, ttn*i
Iti (.iiE. '{lrunS Yuong. !}rrv Nlron) i:o" ir;i 6iii
g.itn giting i: tr€n.
Igoi.i r.a cAr: bqn LSrn.firnil
tjiang,'l'r.{n QuAu, Ngu_v6n }lt\ng Srrn, (rft.f,
Phan CIr;1q l'r'irLlr, Di Nf rrg); Ld II0ng IIenh
t P t"I'l{" Ngu"1'6n I'rri i, IIa Na:i) cit:rg ,:ti i,i1 *'u,
I rl (] nE d6i l0 t.
'l'rrrtr iai c(r : a) i-a L) li tuo rr,, il 11ry11g.
I'idn f;d, : Cic ba n Tlin erri ii, .\grr.r in I[i,
Anlr Ngu.t'6n, l,im l trrrg (iilrrr6, .\grrri:ir Ilrrrrg _
5sn. \gur.6n Binh lrr (plrar, r,lr,1 ir l r inh, I)n
'l'rhn i)u-r Iiinir ii? G. l rulg TrL,rn$I, eu.r.
I:rgl:
lrilirrn), I-)ii rrg Vij Sori, Cao Yi B; (l,ip it A.,
Llll I'H tt$ Noi) t,(r liri giii r6t.
I .\"7
Il-r'
Bel
I
t
ll
o
it.'t4$. fiiii r a hii:n lLran h9
.l
,r i . l'"1rl: - il' ,, - i'#,, ;-
t1
/'-;-
3/-L-
!te- , 1/y' :fi
I
\
lu gugir, I'd ri .ryd u
i'teill,, l4O-.-ChrLngominh ring ndu n ii s6 tg
nhi6n 16 thi ns * I Lh"6ng thE ld s; chinh phuong.
Sd lif c 7'lld,
Bii 5i t{0. Giii Jrtr utrng trinlr
.3 * .3o'r, * !,r9r,oc 3r = o
vrii a lir iharr; sfi ducng..1 Itr tjoc cho trrrhc.
Eit 2lt40. Tinr i{l ri c6c sri ngur,6n E, !,!, z
th6a mEn phunng trinh :
Pd Bd Khangl
, ?t * iy + 1960, =._ 0
Ph*ctng Thoo
Bei 6,, 1,4O. l'inr tit cA cue bi cla thrrr cia.
mdt lri6n sd 1.huc f , g, h, th6e min h{
8ii 3/1{O. Chung rlirrh ring n€u phuong
trinh
.,2
cd nghiQm lhi
' l',.r2) 'r !t{r\'i }r.r') :
I'te) * g(.r'2) + frr.r') = -!
f(x\ * s(J) * rr(r2)= -.
.r'4 .i- e.r5 + brT * ar -l- i = n
'r2+1t,-2)s>3.
v6.i rnoi .r.
Nguudrr Vtin. Mciu
,\'guuin Ntnh Dte
1t
> {1,':l}n. {g,1rs ilrf) . i b, ,rcs {l,ll) " }l;;
. r,rrs {i .:' . ,ila) i ot,
l,-'
t./
B&i ?i tr 4.O. 'i"r6n c{c canli c,la tu gi{c l6i eir
. diQ,n tir:h S, vB. phia ugoil i, dr,rng c{c'hinh vu6ng.
TSm e6c hinh vrrdnS il(r tno thlnh rn6t tu gi{c
c6 di0n ticir Sr. Hfrr' clrring nrinb ring
e) sr.>2"$.
b) S1-= 25 iil:i. r a clri lilrr r:6c dudng r:tr6rr
cfia tL? gi6c han rtSir hing rrhrau" r.A vrrrin$-g6c
yni nhau.
?"hat vdn Il 6i
Ber l0iI4S. flir,, .[ rluirrr.4 rlrar)g rlr az, d.t.
ria-dbng qu,rr tii
{,r. l'u urdt.clibm 81 tr0n r11{
th6c rn$n OB 1* l, ta k6 during thSng song sorlg r(rr
da cfit dz [r ,B2, ttr 82 liir ttrucrng thing song song
vdi d1 c{t d3 6 83. tri f}3 k6 du
tliing /?B1 , t)92, @83...
Goi 6ri : Et?EZ; al=BlOBg l tt'e= BgOBt.
Ti6p tuc quA trlnh ra eo nrgr ilh.v cac doan
86 Rd Khang
r-r7
S =OBl *0ts2*...a Olt+n
sin (ctt g z2 .-:3)
sin (r2 1 a3i
sin cr,
'
+
sin (a1+'a2\
s1p3{i5inC2
sin(ai * e2)sin(a.2 *43)
Bni 8/l4l$. Trdn nrit ph{ng cho m duong
thing song song ve n drdng th&ng c:At tu-v6n tl6l
mgt e*t nhau. Bi6t I ing kh6ng cir ba iluong
th&ng ndo dbng"quy, Uiii met pt.,iug drrrrc chia
thinh mi.r'ph[n.,
Chung nrinh r&ng
,< -(n'; tJ
.
3'{'--',
elsl + asss B$ss = azn|- t aoct DBs'l. =
a ... = Ascz B3g, f ,{res+Afge{"
Ta Yd,nIu
F
>
t
Ll Qtt6t tldn
r#cer sf{}c
w*
YA
ToAt{ H*C
NSI VOI NfiAHH
flff' fts e
$IA }{* KffiSHG
YU THq:
vA su *iA.lifi
,
PH+M EUYf,N
YAo nbftng ndm 30 eria th{ hi nA.i'. vign si
. Keualuso (snu nay t* chi iich f iEn nen iim hh{rr
hge Li6n XO) dA dirng m6 hinh tuan * co tim
duoc ngul'0n nhAn vA biQn phdp x-& lf hien tuong
rung flate ir'eAc cAnh rnA-v trav b6ng liirn loai.
t .\i0ncdpxki ilfi chrng nrinh khi n[ng eon ngurii
cf tht bay t0i c&c htnh tinh xa rdi blng cde
con tilu r'fi tru mang c{c tin lira nhiEu ting vA
ufie ms dr'r cria ro:r ngrroi de tr; tirAnh hi$n
thu c. iAc nhi co iro* rlA io{n hoc v6n ti6p tue
phBc vu n,hlrng e hu,r'6n bay blng cAc- tinh torln
r& 11" c*c'sS liQu vb qui digc con tAu.
llign n*-r' e&'e m&-v Lray titrn kich di c6 v*.n
t6e tre u l3tl0 nr6ti gi0.v tuc rrbanh gdp 4 IAn ti€ng
d0rg, ngu&i l{i ph&i t:6 sric !:h6e qa hf thln
kinh d&m b&o. Tu.v nhi6n; vi t6e d0 phfi.n irng
erla ton ugr&i ld 6,i gi{y n0u trrrr1r: khi kip
ohAn rrng. rnlr trar dli tu,,t guu q,iA,rg .Jr-runS
Y thuAt hing kherng vi drr hanh,vu tru r:6
quan hg niflt thidt v&i to6n hQc vd eo hge.
Dd ld cOng cr.r c6 hi{u qu$ dA gi&i quy6r
e$e v{.n dE cdt ydu ,trong lr; thuydt bgy, trong
tinh to6n vi thi6t kg c{e mAr..bay, t6n ir}a...
'llhmc v{y, v{n rlb ldn erla th6"ki 19 vA dlu
thd ki 20 li c6 thE dua c6.r thidt bi n{ng hon
khdng l
vl tim tluqc efiag {hr}* ldc dinh iuc a{ng cir:r
eAnh F *
PvG. trong d6 p * rrrgt d6 ktrdng khi"
v - vAn t6e bs.v, G - he sd phqr thu6e sio hinh
C6ng cria pr6f in e{nh gr.ri lA luu s6. NgAnh h$ng
- kh0ng lf thu-rdt ra iloi cia giii qtrl'6t tluoe nhiEu
bii to{u k1- thuAt guan lrohg uA e&ng cung c6p
cho to{n hoc vl so hoc nhi6u phuurrg hudng
nghi6n cttrr rndi, ten tubi cria nhi0u nhA toin
hoe vA. co hgc gin r'6i nhfrng thd.nh tuu to Lln
eria aginh htng khOng vi du hAah r.t tnr.
cho ta gili phip lA dung bOt kirn Ioai pha d6ng
6p- thinh vdi phun, Khi e h*v, cAc hgt r'fDng o6ng
chl.y trudrc, hav hsi vA lAm nguQi khung-ngoai
cfra viri phun, gidng nhu mb,hOi gi{t clJco tnB
c6 rrhi0t dS i
liQu c<5 y€u-.chu
rin] hrr.og c6 rh] de *,"y aai. ci.
ron_ t$ru vb tru crrn i,.6 vAn t6c l6n hoq g{p
:,, ldn, oFn ,:Ac phi L'Orrg \.fi rru kh0ng iti khi
rr:ing dicu l,,hrln cr,n tlu rrong m0t s6 tiuh hurlng
l,irrtc ia1r. t-)E liir&c phuc l.h6 khlu dti, irgur)! ta
phrti dL)lg t$r rnAy tinh dign t& vi tlnlr, c6 irh&.
ueng (( nghi D nhanlr hon ngrrdi, kip diEu khibn
cf,c con tlu brry nlranh nh5t. NguUi lil xem slr
rufrt hif u r'fic m&-v vi'tinh nhrr rn6t .:r-16r: c&etr
rneng lii thuAt.
lii, thuAt
rAt cao*phi.i c6,.d0 bEn lril rnA trgng lugng
phiLi cryc nh6. T{t c& cAc .l
]I6-v r i tinh eon dring- r6ag rAi irong k-t thu$.t
phdng ltlrunc nhtr dB riiEu ktriFn c{c _t0n lira
ch6ng t0n lfrrr" t0u li'ra ch6ng nra.v bav... lS6u m*.y
l:a-vrcii.r tlrIi phuong cirng tr',rng bj c6c rni.y tinh
ttri d6 ln cugc ehidn aeu !itta lia,i mA.r ririh bay.
ilai to6,n diEu khiEn e6c thi6t bi ba-v. i:6 nme ti&rr
dI riuoc vi{n s'i LiCn 5,} i,intriugyrr tr.inh birr
tl1]*g ciruv0n liir.4-i: ,, l.-i t irrrldt rliilu khibn iiii.rru s.
Yr€c r:l:8 t*o ri t6 ,,hu, san .rrrfri r:hc fhiSt
bi bal.hig;r dai i:iing iA nirir.;r; bi rlit gu6c gia
drcc tl.rrrc hi6n lh*o cic p:i*Lrng 6n c6 e6c tinh
toirn io$n hr:e v& cG hec ihi,rh xic. d) day nhtog
rnAv tinh diBu litri'6n c[e r:ra-v e0ng cu va aey
chu.vEn s&n xu6l, circ rnAi t iirh ki'trn tra r:hSt
I rru trrl...
C&c.rtrlri phur: ph&n lrrc lirolg thE i&rn b&ng
kinr ioai vi &it ti6n r'{ hh0lg c6 kinr lo4i lio
chju ilugc nhift d6,l€00o
ilont'ram n6lg r:hiv
r'r nhi0t d$ 3100o). CAe nghi*n rrrrr cu-ii--hde-tsen
Qtra il&v tq thfrr, ha.ng klrong vd rlrr hd'nh r,I
tru lir k6t qua lao dOng cria hdrrg .;4p nhA. b6e
hoc vd chuy0n gia crla nhibu tin tr r.r.rc, trong
dl6 c6 c6c nhi loiin hoc. co hoc, r.f,t i-f hoc. 6
tl{r'cry hoc r.ir tohn hoc il6ng vai tr.d quaa trong.
l-ao d6ng cria hg rI[ bi6n c6c th{nh tuu m(:i
nh{t cira kho* hor: r.ir ti_} thuAt thinh hign thrgc-
d6.lA. cdc ur6..v bal, hign dai, e,ic con tiu v& trq
ehlp e{n}r cir,r een rrgrt$i rrit ng6n khoing cil.ch
tdi r.,ac r i s:ir, ra xoi...
Tr*.o dl$i s&f bqn dor
{qH}ts trerj H{}E r{rHs }r{?*
Hr* rUYEru $I$rE
?ffi*trS SE THi TOAH fiHffI A
B&; Wqe ts84 * r9E5
TA V,{N DTNH
Ud, nhirug bAi tOi gep rr.<.rng rlip
'tuvBn *irih mrln tofln i0i ed mlt
xdt rnrrdr: tr:ao ffhi vrii c{e irlp
cir{m thi
vdi nh&u
1r6 ytu
toi^n.
'!iruirc hdt..rin trich ra il:ly plr{n
[.'.6
I
I
I
I
I
I
J
I
I
[
I
I
f
Ii6n quan :
d6 8C-a,
pking n&i
)
arta BC ud lD D.
{
'l'Oi xem nhu c{c ban dE eh(rng minti dugc
llD I Erl yA troRg quA. trinh d6 chunp rninh
dusc EC J- m{t phfrug (dnI) vi d@ do Bb LIt
ler*,
dlu lidi ctl
l''
I
B&-y gi+ xirt iiit) csu h6i 1. Cic hqi gi&i thli.orig
ldm iheu mfit trrtrlg hs i c!1r,ir sa ri :
Tai sao lai phii lOi thdi lhu I'h"v ? Pl,:1 ii ti-ir
lfeil fiu e lriruii to il .lu J,r. 1tr-r' rrftiin, t,',i rirrri, n
ili rrrlhi cit ilan sui' nghi therrr !'6 hai thi dri
s:i ll :
'i-hi t!rt 1. 1iii,r. linr d!iiiu kril ilii lrri tarrr giac
i:rl diBn tirh *iing nhsu. \t:rr tr',i ltli r ( Ilai !em
fi.r: [fi,,* n]rau thi co diiln lirir i,;1ng nhau,,,
rri rt\ng ld, rr)ri rth s(rl 1{1 llljirir truirng hop ii:ri
tanr gilc ir',,1;,'ir ii,'ir ir,it.,- nl':rri.
Cde,,r thri lii?lr: Yi dri cti fJ _i_ 8r-l n€n nrri,ln
L/ Li t1 vge r.: irrr 1iC v:i ib iiri r.hi ,,An /.1 'L.{/r
nt"r*. l.rii: rltl trLm uiric ilI) cri I./ vr'rn lii trrrrig
tii-r itt r.ria li dtrring- (.it f) nin 1S tiinr qieic t in vi\
r:l1i ii,i Il = LD. Srrr 116 h:ri iarii giiri: .4_IB vA
iiiii
lrrQng 6 l, iei rti 18 chrrnq- r.ri 1.1 = Ifi
ne:r r,irfrng lrin0 nhllu. Oc riir .111 = 1] jJ hal
&.c,
'['rii tli-r i'r'r l;1 I r.lirlg l:ri, i,ii li:ii vi6t tlrdrr; :
Vii,r /./ lr) rir-qc t.ri:,i lJr'. v:tr .{1) lilii [:'r.
T'ht dtt ?. 'l'inr rliiu kiFn ,13 :rr, l ritlong thirrg
vnBrg *tllu r.rii rri6t m;t I)lr:tnr.i llibn nhitln Ii
rruiirt rltrr)'ng ttl'ing 1) r'rrirng grir: r'i'ri mit phi.ng
(l',i tlr.i /) pirii rru0nS g/rrt vi;i it irhiit milt ilrrdtg,
liririg eira rnirt phling (fl. Ne,, trr d,i ta k€t
lu4rr
:ing tiiEtr ki0n.,it rrrdt. r!rr,'rn;f tl"nr ',rrr)ng qrir
vrii trtit' rnIt phirrg 1& nl' r'rii,iig f,i.. ',-iii !t nhdt
trrrli rlrrrilrg ttrEng erl:: nrirt phins iir i rii rirrrg
I; liiri.:q ilting.
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r; rir ili r.ri rr hii ( .lirn
{lach !hr'r hti:.'lrtrr'rc lrii lhtin r(:t: Ii.lii i=i
tlri "I.l 1r\ tl i g1' 1.i1i1 iJi.' r d .,t/) ri)i t:lrr'rng nrinh.
,.iiir sr', i) c ltri.1Ji:: /)li, srrr r',r lr:ri trrrrr;i,:,:
vrr6ng ,iI8 r.it 1,ti 1i b.iirg nir:rn ivir:r) r.nnh huy€rr
L:ilti1 irlrlru vi 1Ji , lliitri), rio rlr'; .i.{ .: ^il}. sil}'
Lu l:rri 11iirr: .{i/) i.liri. \:rl irltDg trrlrrr L/ r"rinq
iiii rlrr'iiiril i'rro, r:..1iiiil ii 1/ i" ,{/). ir,:l lrrp. r'i;i
Liiiu ilr-i cltr.rirg ;r:i1i; ir it'tl,r, l,/ l_ St; la su.\, t.d.
U lA iivgc. .U(- \'i .1 D.
r:i r:, Iig rr :i t lr]r' r'i ng :
diPir };iin r,i i r i c dt I,i
li dlgc crirL Ii: ','i dI] a ciis ir:rri pi,ii i:i3u n6 rri
nilhia iA : i'ir.,-r rliEtr lii0n vb lr I'i. c e iu vi dri dP
/./ li di g.r .'iia Bf-' i,i ,{Jl. i(hi lunr niii .rrr: ban rhi
tirir r:L rrliil iiibl [i$n dri thi eing chrrt r11ng mii
phii l:1nr thd ni\o tim dluoc hit t.'1.,: tliDLr kiQn rli.
Y:it- trr rflt re nhirn x$t slru : Carr h,ii r Tinr di?:;
ti6n uP... de... )) tlrrlc rhit li r:r,",t c..iu hi,i yE
tllEu l;it n fit cit ud rlit.
Cirng e6 nhin xd.t irr,-rng tu ildi v,;i (4Lt ltdi i
Viv lilrr lhr:r.i i rii'h ;ii)o l.- ,ir'l irg '.,
ilir. gi* r1.1, xong k-i ti;i. Ilirrl: linir nr0t oiirit
tide-_<:rrr eirn hlti lriirlr hge: tGiu sir l--cs
rt't 3 i' l' 'l'inh gdc d.rrfl hinh chrr rln,.rq iiinh f.r'
ti6p xric vrli 1111rir',* ttling r.D,). 1)a-1' cing li rnqt
ceu h6i vii d:i\Lr lii0n 6t r,5 i,J iiir. r"hrrn3 thudng
t6i chi 1lr::i.; r'lir: l-rii ll)rrr 1,i:dn i[ (,i',: x.nt.nht
hinir riri tltranq kirlr /.i il;'r tiitr \r'ic 1r;i f.'IJ rbi
iir r'1,1 tinh ittrrvi sin (a,11; .: (/';--
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'I'rotrg sd ni;iing l.iiri t6i chrirl tdi ctrrra th{r,
irui rii,: rir,it ;rh{t ti} giI thidt rin (a :.:) c0 gin
Ili nhri ',:l-r' r'iii chr'rrrg r,nin]r r.ins iriah r.{u
rirong liini: Ll tidii xLr* viri (, 11. Xin ntii nirir
th0tn: ridrr ji;rr vi0c rir'r thi r:i.r' liln t,un phdt
iriQn la ling irinh r:iri n6i tr'0n lilr,';ng nh*r:g ehi
tiFpr rric ', ui CO niir ri.rn liIp riii: r'iii BD, i.',4..
B-l r tr lriirn nhiEn hinh cln nrr,v tiip riie v*i "'lJ)
vi RC, nghi:r ll'i rti tif,:p *ric vr'ri ,.;i r:irr crrnh
r:tie tr'r rli,:n -{i.i{,iJ.
C{c ban c&n dpc ktt r:ria idi trutie iihi lim d}
V{r'p}rri i lrirri ci. lr:ii c'lii,li, vl n8n liiirr,.irci'r
tlrri nlriit ilrrirc rlt :rrir: rlinh tli?p !;iltr rll rri r.ll I,/
Iii ilvgc cirrl lifl vi Cl) lr-\ D s c, r'i',i rAch thri
h:ii r-:hri'ng nrinh ti$p line chinh 6 = e *irnq ii
di2* l:iit dri ,li\ 1.r iz1 11 r {e ,,i'rri BC ri l{i}. l.r\rn
nilrr rl.\. t(r'r: il'r cl:ri,iiri ininh rirg diEu kian at
ct't pii tlii tli', J./ i* rlvge cria rgil yi .{/) lil D : c
iirc ii I xc lii tliFu kign riir dh I./ iir ilvgc t:iie
.6{,) r.i .'t} I'ir ngoii r-liEu kifn 6=c ra,kh6ng eitn
diBu k;qiri nio i.:h.jrc vB 0, e l.irrn cho Ll lit dvgc
i;ria BC r ri I /) nin:.
,,rilu l/rqil rd rrdi dunq c&e. ctu h6i.
$AH pfir fl$ffir$e{ r0r Bfit roir
fr$'f#s#e &"#
rranr iii l rcii qur, rrri 1i1fi1 iiri tciiin
|)t:
.r1,rr,i]
tL;i r ln ct)rr rrlrii rrrii i. Blirr irril' lii:; eric c,lii
td li l dtn I d? lao ttrdnh biln sit I md1 ,td cd ,l
i4
:t) I ir,t Ilreir t.il,. li llrrt rrlr.', I trri' i.r ,.irr'irrg rninlr
rltsc rrirrg nilu 1./ la rlvgc crla #/-.' vi ,.1,I.} tIi
ir=c. lrjc li rnlri r.hirng nrirrh tlrro,: i'lii:u hiSn rii
cri dB /./ l:\ dvgc cira fiC vA ,{1) li } - c rni.
clrrru hi r.l;i r10ng ridn nrgnh rlB ( lihj h = e thi I./
li rlvgc cri"r 6C vd i D D. Cho n€n chita r1ii.
h,t L.{nr lhe<; c:1ch thri }rri til:L: lir chir.lg rnirrlr
iltrryr ritg ndn b * c llri /,/ lri ilvgr: t:iia l}1,' r'i
.-iI), iric li tim il ft$t m7t tiilrr l;iFn ifui rlE Lf t,i
dlvgc rira E{,' r'ir dI}. l)rfnq }ai i iliv i.iroq chir:r
clri vi r'hua th'F hirlt i'l cq ngo:ri ,lir'.Lr 1.. j1'.s |=6
r:t t:r: i'i)r rliBu iii4n :i:rn lihtr: ', l- /,, u .!irl cirrr
f"I l*. dr.g,-. r:r'ra fi{"' vl .{I) nii'a ii}rr}ng.
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cnn sd ud ba sd eri ? chr?' sd soo chci iich efia
h,ri $ ndu brtn6r llrir cfio hal ad kio.
khi drlng brlt in* c6 l.hB. n6i ring: < Rir i toin
ahi cl ng&n :{y nghiQrn D' yd.them m$t ai&nr vui:
( tlong tl6 e6 rn$t nghigm crls minh ).
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ngnl 6y, ttri .,uri r;'l shu rac ban. \'A lrri roin
,ii h{u tlir, tOi r,ir rirOt sr}c manh rl:,1 ,rtvur.
:(u!.t trign tu lirr nirrrng rhr* duoc giii qu3.&i
tld)n vetr, ud thu,.stlJI
trO thilrrli rri,.,i tlrfluh
thric I ft.ong cudc ch1.t, dua tirrr nghiQrr: cho iieh
tun hon li.hi cli,-ra i:o r-:;,rt:h gi ,18 i.irn iir.rr.y,:: turin b&
rie nghigm. ng-uii t* dS phit higri drrr;,.: t:lrin
nghiFin sarr dir':
l)irng trn&e bii toin c6 diQn rflt r$ng,'lai c6
tht *l.r nhi&u rghiQrn. r'igc tim duoc mQt hay
hai rrghiQrn lA clang t1 iri : irhrng d{t ilugc co s&
tj' ir.:&n tl't tri d6 qu6t sr,:h rrroi ng6c ngActi, trflt
drr*i: toi.n !0 e5c nghif rrr .'drr qul hul. B&i vi
u6 drii hiii phi.i e6 rnr't l;.i:r linh vurrg vAng,
ilr$i cieh rrhirr vu& buo qilrii, r.'rjra siu sdc. 06y
chinh li rtiFu toi ruu6n n(ri voi c{c ban.
H6m rral'. tiii lai gqp nrQt bAi to6.n:
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[:an rif thdy bii io{.n niy c6 hg h0.ng v&i c&c
lr*i (i ll:irrq b* ifln i'ilr r. ? \{tii cAc
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crio fr,;i rreig pirrii kftdni7 i'r,. hhi dii, ci:e cAri
dS 1r ,ri uhu trong liine.
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lt{im 197 1, tai Ih$1, nqi;,'ri te iili riir,*i, ngtri8nr
r:hn tlch ltil hrln nil'a. '] air riri ( l.rrong tril I e fra
t,i'.u X0 c6ng 116 iin dd rJ,: nin, iiiiij. nhrrrrg
gi'i iii rn$t fil,-, crln s,',, l:il ir;i;: ";".116. iiii Yi$t
*-nnr. l.tiiu n rr: l9i'1..;,:rl'l''.r iilr:! f.liiirre (tOp
1U shul 0n loln, Dqi il:;i: !:ii :ri;lirr; J1, j:iA i.igi
nay li Bqi hqe su piinru iir\ f-0i ii i irl .t ir3;rr
d*gc nghifrrfg,63l >{' it = SE )< ?t = ?.liii. r'a i;*n
Y& *)rnh l{da (cuiig iiipi ,ii ohf ng liirrli ngt:iii;,
ttS elio tich l*n ailr'!I irodg trit e& rjer. ngiriiir;r
r,i iir8 ,.'6 ci,a ir*, t,r ,n, r Cid.i qu.vdr tr t,i: r'ril lA
{'igu chirtrg trr r}ri}iif ri:uriri. Nhuilg tr..oIg iiiri
ehrr. l&rl ilugc r;{,,.Jo,,udi,liEu r€it
iir uiri6u
ld r!i lirrr ugbirir,, 1r:' n[1'11 r,. US lA ti,, kBri q,.ri
r,ia t*c iral 1up lii { f . SiiSP 1I, {{S llgi, c1{ng
I r€fi bio i ,r:1:r ir.iL: r.E tLiii; ix.il si'r ?'i i 1-Al1$?{ }.
f i;.era loi got _l' rli'r".1,,! ir:1i tii"v r,ar* tirn ngl: it\nl
b8 uh{t, nhur:5J r:ga.; iii r:iiir':rg phrii $[u, l,.rr
i:h.ipt th{y le i0r rl;n iluuog ,i:i* t*i rilri; giii
i${n lJd tr*i ioan. }1i', '; ,,1 t,,,, 1}':rr lglri$rn iri i:iifit,
tdi hy vong llnr iirroi'i'ij.l'::i i,jri iirrri. lX'irS l$r
bii toAn di hidn cae buhi i ';i vi irr;:e ltir: gii.i
Iau lrong thiri hi ti'ri tli l:ro d,)ng tir*.lir thfr'nq
gio phtlt ray Lrf . 'l 0i hh*ng lori l,ri6t trsi drit
gi nila, vir E::ic nghif rn sr1 ibn 1uo'. hi&n l*n nhu
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Liilir nghi6rn. 'i illr: tiilr.v. dri lr; r:qhif rrr
r--irng.
t'h$ J:i s:iu lrl nB*y kt tri irir bidt ]:r:r i*5n, t$i
rltr clrinh pht,'d;t,7* rr6 Sring lrrl'r4g |151 bo*
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Iir.) Ll tl:]
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cO giAil trrolg Pfub ttr6ng trueg ligc Tlung
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5. fi6 'lrong Yinh
l.0p 1l : 0. lt{guy3n Hoanh Currnq
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fr*rFffie *&{ ffiffi&y r* rffr* Hffi#ffi& ffi&$fl rqs$
In- 15.000 sd t+i xi rigbiep in 75 HAng Bil * I'l* Nqi. Sd ia ?4/&t, Iu xo6g vn grti ruu ehilu th6ug $-xBB$
&hi adr tI&S4
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