thoi m6n hai di6u kiQn dd cho. D
FNhSn x6t. Bdi ndy tlugc tl6ng d6o c6c ban tham gia' Tuy nhi0n, m6J sd ban sau khi tim ra ktit qu6 14i qu6n thir
lpi. B4n Nyrye, Hftu Hodng,gB, THCS Trin Phri, Vdn Hoii, Thanh Hoir ddn6u ra nhfln x6t c6 th€ thay si5 33 0
tliOu kiQn 2) boi sO m vdi m > 32. Ngodi bqn Hoitng, cdc
ban sau dAy c6 ldi gi6i tdt:
Nam D!nh: Nguydn Tuiin Hmg, 10 To6n 1, THPT chuy€n L6 H6ng Phong; IIh Nam: Bdch Xudn Dqo, 11
To6n, THPT chuy6n Bi6n Hod; YOn Brli: Vil Hing
Qudn, l0 To6n, THPT chuy€n Nguy6n f6t fnanl; niic Giang: Chu Thu) Nhung, Duong Vdn Thdng, NguyAn
Th! Phatntg Lan, l0 To6n, THPT chuy€n Bdc Giang;
Thanh ldLohz Trinh Hd Hiing, 12T, THPT chuy6n Lam Son; Hit Tinh: Nguydn Vdn Th6,10Tl, THPT chuy€n
Hd Tinh; Quing Binh: //gd Hodng Thanh Quang, 11
To6n, THPT chuyCn Quang Binh; Long An: Nguydn
Minh Tri, llTl, Chu Thi Thu Hiin,12T, THPT chuy6n Long An; Vinh Long: Trdn Duy Qudn, llTl, Chdu Hod
Nhdn, 11T2, THPT chuy6n Nguy6n Binh Khi6m; Gia LaL Trdn Nguy€n Try, 12C3A, THPT chuydn Hr)ng
Vuong, TP. Pleiku; Tidn Giang: Chdu Hodng Long, 11 To6n, THPT chuy6n Ti6n Giang; Dik LIk: Nguydn Tutin Hisp, 11T2, TIIPT Ngd Gia Tu, Eakar; Bn Ria -
Vfrng Tlru: Thdi Ngpc Anfu l1 To6n 1, THPT chuy6n L0
Quj'Ddn.
NGUYEN VAN MAU *Bid Tlll435" Titrt tdt ca cdc da thuc Ii'';'l')
sao cho T (x. v).7 {:. / i '= ,i ('r: + yl, 'xl + r'-- )
'u'ti'i rrit2i x, !, Z,t thu6c R".
Lnn gini. (Theo bqn Chu Thi Hiin,12T, THPT
chuy6n Long An).
. X6t trudnghqq T(x,Y) * 0. Nhfln xdt
(xz + Yt) + (xt + Yz): (x + Y)(z + t),
(xz + yt) - (xt + Yz): (x - Y)(z - t).
Do d6 niSu ta dlt
T(x, y) : (x + YY@ - YY .Ux, Y),
trong d6 m, n € N vd da thfic Q@, Y) kh6ng
chiah6tcho x*y,x-! (1)
thi T(x, y).7(2, t): T(xz * Yt, xt * Yz)
a (x + y)*.(x - y)".Ux,y).(z + t)^.(z - tY'q', t)
: (y + yf (z + t)*.(x - yl .(z - t)" .Q(xz + yt, xt + yz)
a Q(x, y).Q@, t): Q(xz + Yt, xt + Yz) (2) cho z: t:0 thl Q@,i.QQ,0) : 0(0, 0). Ta chimg minh 9(0, 0) * 0 (suy ra Q@,y)=l)' Thit viy, gii su 0(0, 0) : O.LdY Y: -x, t: z'
Tri (2) ta c6 Q(x, -x).Q@, z): Q(0,0) : 0. Xet QQ, z) + 0 > Q@, -x): 0.
Khid6 QG,y1: lauxili
i, j
=1a11$i- (-y)')yi +\ou{-t)i .ti
i.j i.j
Q@,-x):o =' \o,,*i1-*)/ = o'
i,j
Suy ra Ux, y) =\au@i - ('y)')yi i (x + v).
i,j
Tuong tu n6u Q@, r):0,Y2 e lR thi ta suy ra