Tdng c6c sd tir i ddn3g lh I = 3T0
= zgo. 2
Goi ni,r,,s; (i = 1,2,..., 13) li c6c sd trOn m6i
vdng trdn. Ttr gii thidt bii to6n suy ra tdng cilc s0
theo m6i vdng trbn :
T<ing c6c sd theo m5i dudng thing hu6ng t6m lh:
ni + r; +r, =l = 60 (i = 7,2,..., 13)
' 13
Ldp bdng tinh :
6 aaY ,, *si = pi = 60 - ni (i = 1,2, ...,13). C6
nhidu c6ch phAn tich pi=ri+si vdi ciic rhng bu6c:
14<r;<23, I <s;S 13,s;+4< rilni-4(i=t,
13
2, ..., l3). Vi It = 60 n6n chi cdn chon c6c s6
i--1
n; vh s; dOi mOt khiic nhau nhu bdng tren. MOt
phuong 6n chon vi sip xep n;, ri, s; tr€n m5i vdng
rrdn duoc rhd hicn 6 so d6 bon.
Neu s6p xdp 13 so trOn m5i vdng trdn vi chon
c4p @i, s) khr4c di thi ta c6 cdc nghiOm khric.
NhAn x6t. Nhtng ban sau dua ra dugc nhidu ddp 6n
dring, trinh biy 16 rang : Vinh Phfc : PhamThiThiry
Ng,in,K27C To6n - Tin, DHSP Ha NOi II, XuAn Hda,
M0 Linh, T01I4 Ngot, khu 8, D6ng Van, YOn Lac ; Hi
NQi : Ngrzyln Thi Thu Hd, ll{2, THPT Ngoc Hdi,
Thanh Tri; Hn Tay z Ddng Xtdn Nam, 10 Tin, THPT chuy6n Nguy6n Hu€, Tx. Hd DOng ; Tp. Htrd : Mai
ThanhVdn, I 10 Thach Hdn, Thu6n Hda.
udNc euANG
riXH GOC
Bang c6ch c6t di m6t hinh quat ACD cia mlt
tdm bia hinh trdn, sau d6 d6n khuat h\nh OCDB
sao cho hai doan OA, OB
tring nhau ta sE dugc mot
vQt dqng hing c6 dang
hinh n6n. NOu ban mudn
lim m6t vAt drmg hhng
nhu tron c6 thd tich l6n
nhdt thi g6c b am AoB
phii bang bao nhiOu ?
BUI C6NG THUC
(KhoThdnh phdm,COng ty Mabuchi
KCN Bi|n Hda 2, Ddng Nai)
13 13 13 'r
ln;=lr;=f s, =a = 266
i=l i=l i=l J
DB B ll 2'7 28 29 30 3l 32 JJ 34 35 36 37 38 39 Pi= 60-n; 3i 32 31 30 29 28 2't 26 25 24 23 22 2t r; 23 20 22 l1 l8 25 26 24 21 t9 15 16 14 Si t0 t2 9 l3 ll J I 2 4 5 8 6 '1
DA CI{INH XAC ."" CHtiA ?
Li€n nhd Long giii h6 bli todn :
Gid s* a, b, c ld dO ddi ba canh cila m1t tam
gidc. Chtntg minh
21a2b2 +b2 c2 +r2 121 < al+b++c'+abc(a+b+c) (l)
Sau khi suy nghi Long dua ra m6t ldi giii : BDT (1) a ab(2ab-c21+ br12br-a21+ ca1zca-*)
.oo*ba+ca(z)Ta c6 : Zqb - & . o2 + b2 - c2 + ab(Zab-cz) < Ta c6 : Zqb - & . o2 + b2 - c2 + ab(Zab-cz) < Tudng tu: bc(2bc - a\ < ca(2ca - b2) < (bz +cz)(bz +cz -az) 2 (cz +az11cz +az -b21 (4) (s) Tt (3), (4), (5) suy ra BDT (2) duoc chfng
minh. Do d6 BDT (i) duo.c chrlng minh.
C6c ban thdy ldi giAi cira Long d6 chinh xi{c
chua ? Cdn ldi giii cira ban ?
TRANNGOC THANG
(S/ K50A, khoaTodn -Tin, DHSP Hd N1i f)