NIuc Ban doc tim tdi nhAn duoc rdt nhitiu
cr{c bhi vidt v}, d6, cAu h6i cira ban doc' nhat
6 ;; u*n t o. sinh. Dd nhidu b4n cd thd
tham gia trOn b6o, chring toi se lAn lucn- n€u
"a. iai, h6i cira c6c ban.-lvloi ciic ban o khap
*"i "rieriri nu6i giri cau trA ldi vd'(ban nhb
ghi sd c[ra cAu h6i). Chring tOi s6. chgn dang 66c cau trA ldi kbrn t6n, dia chi ci{c ban' MOt
cAu h6i c6 thd dang nhidu cAu tri ldi ndu hair'
Ciic cAu h6i ki nhi, ld :
1.(3.04). Mr3t cudn s6ch c6 bhi
minh rang bidu thric
A =.r5 i 3r^y - 5x3.v2 - l5xrvr + 4t'.vo
nhin moi giri tri khi{c 33"
"Chrlng , r.r..5 a \L)' 2.(3.04). Bat x>0,yr0gqi vir dd giAi : "A = (x+ 3y)(x -.vXx + 1')(.r - 21')(; + 2l) vi 33 = (-3X11X1X-1) = 3(-1iX-lt(i) N€n A + -13'.."
Xin cho i kidn vd bli nh;r ?
(Iv16t ban khOng ghi ten)
, .rr \'
dang thtic ^ > Vr.v vdr
L
li gi. mang tOn ai ?
(Nhidu ban h6i).
3.(3.04). Gi[i phuong trinh -t' - 3r + 2 = 0
GiAi : PT trcn tudng duong v6i t-- !
(x-lXr-2)=0c.'l^-jlx =2 lx =2
C6 hai ciich tri idi :
VAy phuong trinh c6 hai nghiOm :
.tr=1r,hx=2 (1)
x=lhoac-r=Z (.2)
NOn chon ci{ch ndo ?
(Trdn Thi H, Di6n HOng, Di€n Chau, Nghq An)
THTT
Gidi ddp bdi :
e0 qfi THVY sl o6 snlrl
(THTT s6' 3lB, thdng 12 ndm 2003) Tba soan nhAn du-o. c kh6 nhidu ldi giii cho bli
tp6n nly.Tdt ca ca" ban ddu dua ia c6,ch cat
gh6p dring theo y6u cdu. Dudi day ld d6p 6l ctra
Aai'CA sdi Th,;y Si dd'ban thd hicn qua hai hinh
ve thinfr t tnd irien yeu cdu thrl nhdt, hinh 2 thd
hiOn yOu cdu thrl hai ctra c0 g6i).
Hinh 2
C6c ban sau duo.c nhAn tang phdm ki niy :
Nguy€nTudh Linh,10 To6n, THP| NgyVln Tat
Th#h; Ydn B6i ; DuongTrung Hiau,l-lB.THw
NK Ngo Si Li0n, Bdc Giang ; N-guy€-n-Thi Thu
Huv€nl,11A Sinh, DHKHTN - DHQG Hi Ndi ;
Npuv€n Npoc Hd.7/3, THCS Lc Qui DOn, Tp'
HEi buong"; TrdnVdn Ngoc Tdn,93' THCS Phan Thric Dicn] Dion Tho, Dien Bdn, Qu6ng Nam'
g6NC QUANG
26
riU NCAY SINH
Vho nsav Oudc td Phu nfi B-3 minh ldm quen
,Oi moiU'an-eai .dt do thuong. Ivfinh thir h6i nsdv sinh. han-e viet cho minh con sd 244 vd n5i ;6;'v h t6ne 6ta l}ldn nghy sinh vdi 31 ldn
th6ns sinh dtra em". Minh chua nghi ra ngay nen ?at bOn chdn vi cdn phii bidt sdm d0 cdn
iane hoa cho ning. Cric ban hdy tim.girip minh
ngey sinh cira cO dy chng sdm cbng tot'
BUI CONG THTIC
(KhoThdnh Phdm - Cbng tY Mabuchi KCN Bi€n Hda 2 - Ddne Nai)
Nguy€n Minh Thdp, 10,{1 Toi{n, DHKHTN -
DHQG He Noi, Dd )tudn Chi, tIA4, THpT Xudn
Dinh, Ttr Li6m, Hi N6i ; Ngzrydn Van Ngoc, l0 Li, THPI chuyOn B6c Ninh, Bdc Ninh; Nguyin
Ti€n Dfing,10,41, THPI Thanh He, HAi Duong ;
Nguy€n Hodng Minh, lOA| THPf LO euf DOn, Tp Quy Nhon, Binh Dinh.
NGOC HI6N
PT{AT CHANG X,A ... NUruC I
Bii todn : Cho a, b ld hai s6'daong vd x, y, z ld cdc sd duong tiy y.Tim gid tri nhd nhd'r cia
bidu thr:rc
Gitii ddp bdi : PHAN vAN
(THTT sd'318, thdng 12 ndm 2003) NhAn x6t rang vdi hai hlm y =f(x) vd y = g(x)
xr{c dinh rrcn R thi tir min/(x) > maxg(_r)=
xeR *.n
f(x) > g(-r) (Vx e R) li dfng (nghia td flx") )
g(r,) v6i moi gii{ tri x6c.dinh x. rhu6c R), nhrmg
di6u nguoc lai chua chic dring. Day ld nguyOn nhAn chfnh d6n ddn sai ldm. CE the duu ru"pfian
vi du sau :
V6i hai hlm/(,r) = sirlr ; g(,r) = -J2n"og
xdc dinh tren R, ra c6 : f(x) > g(r) (Vx e R),
nhung min /(x) = -l q maxg(x) = t-r6. Nhu
xeR xeR
vay ta rhay ring DK m > t+Ji 6 ldi giii da
dang chi lh DK dfr md chua ld DK c.dn. Vi vAy
kdt qu6 tr€n.chua phii ln Ap dt ch c6,c gia iii
cua tham sd m dd bat phuong trinh d"d cho nghiOm dring vdi moi x.
Gidi lai bdi todn: X6t him/(x) = sinr + cosr.
5 ( . t)2
- stntx =
a-1rrn**cosx--)
TOn tai x" dd sinx, *coSJ, =
Suy - ra max /(x) = I. Va,xeR" 4 xeR" 4
qp@a
t4- y2
(ay + bz)(az+by) (az +bx)(ax +bz)
2
Z
(ax+ by)(ay+fiy)
MOt ban hoc sinh dA giii nhu sau :
DO ding chring minh duoc :
(ay + bz)z < 1az +b211y2 * 12 )
Tucrng tu (az + by)2 < (a2 +b2)(r2 +y2)
v4y (ay+bz)(az+by) 2 x 2 x *2 Tuong tu y2 (a2 +b2)(y2 +12) 2 v
nghiOm dring vdi moi "r e r? thi DK cdn vi dir ld m) max/'(x), hav *> 1.
xeR- 4
Rdt nhi6u ban d6 chi dring ch6 sai cira ldi gi6i
bli toi{n vI hdu h€t cdc ban ddu giii lai bang fe
dao hlm : rim gi6 tri lon nhdt ciia himf(x) = sinx + cosr - sin2x tr0n R, hay h)mflr) = f(x) = sinx + cosr - sin2x tr0n R, hay h)mflr) =
t21r+I ran l-Ji,Jil aCsuy ra kdt qu6 dring li
. Sau ddy ld c6c ban c6 ddp i{n tdt hon ci:
(az+ bx)(ax +bz) 2 z (a2 +b2)1zz +.x21 2 (ax + by)(ay + bx) 62 + b2 71xz + y2 1 Do d5 ./1')-r\ M> 1 | *' * !' * ,' ) o2 *b' \y'+r2 ,2 +x2 ' *2 +r2 )
MIt kh6c ta chring minh du-o. c :
,212r23) ) ) ') r a -a ) ) ) ') r a -a y- +z' z' + x' x' +y' I Suvra M> 3 ' 2(a2 *b')
Ddu d&ng thrlc xiy ra e x = ! = z.
Vay gird tri nh6 nhdt cta M h
#+*)
C6ch trinh bdy tren phii ching ld ... dring !
Ban giAi bii torin ndLy nhu thd nho ?
NGUYEN DUC TAN
(Tp. Hd Chi Minh) 5 4 1 2 dd BPT dd cho 5 y)- 4 27
Todn hoc vd Tudi trd
Mathematics and Youth
NAM THU 41
s6 321 (3-2004) Toa soan : 1878, ph6'Gidng V6, Hit NOi DT-Fax:04.5144272
Email : toan hoctt@yahoo.com
oo o o
Dinh cho Trung hoc Co sd - For Lower
Secondary Schools
Trdn Vd,n Hinh - Chuydn phuong
trinh vO ti vd h6 phrrong trinh hrfu ti
Tieng Anh qua c6c bii to6n - English
through )Iath Problems
Ng6 Vi6t Trung - Bei s6'66
Dd thi tuydn sinh l6p 10 chuy6n To6n
Tin tniong DHSP He N6i nam 2003
DO'thi hoc sinh gi6i to6n THCS Tp. Hd
Chi Minh ndm hoc 2003 - 2004
Chudn bi thi vho Dai hgc * University
Entrance Prepara(ion
Dd.ng Vu Iii - Hri6ng dAn giii d6'tri 6n
thi so 1 (tidp theo ki tnrdc)
Nguydn Anh Dilng - Dd tr: 6n thi sd 3
Trdn Manh Htng - Vd m6t bdi to6n
tinh tong ^a TRONG SO NAY @ @ @
Phuong ph6p giii toiln - Math Problem
Solving
Pham Qu6t Phong - Phr.iong trinh c6t
tuydn ciia drrdng cong (tidp theo ki tnr6c) Dd ra ki niy - Problems in This Issue
T7l 327, ..., T8l 327, L7, L2l 321.
Cudc thi giii to6n ki ni€m 40 nam THTT Giai bni ki trudc - Solutions to Previous Problems. GiAi c6c bdi cua sd at Z.
O Tinh todn c6ch nio? - How to Calculate?
Vil Kim Thiy - LI6c h:ong vd sai so'
Cf,u lac bd - Math CIub V6 cAy to6n hoc
fdng UA.n tqp ,
.
iffn E;,r*-ffi,"o${
DON DQC THTT SCi SZZ (412004)
. CuOc thi gi6i todn dac biCt ki niern 40 nnm THTT (cric dd tiep theo)
. Dd thi tuydn sinh ldp 10 THP| Chu Van An vi Hh NOi - Amsterdam 2003
. Hudng d6n gi6i dd thi tuydn sinh l6p 10 THIrf CTT DHSP Ha Noi