L*r6 ngodi vi6c nim chic kir5n thirc c5n bin, n6n tang nhu dinh nghia, dinh li,, ...tacdn cAn phdi t6p ducrt, rdn luyQn k! ndng gi6i quy6t nhirng bdi toan don girin hon,
vira sric hon. Nhirng bdi torin ndy d6ng vai trd nhu nhirng bdi toiin trung gian, vd vi6c k6t nOl ntrnng Ual torin trung gian ndy m6t cdch hSp ly ta sE nhdn du-o. c
nhirng bdi toan hay. Cdch ti6p cfn ndy r6t ptrO Ui6n hong hgc todn, nghiCn criu to6n.
Bdi vi6t ducrc trinh bdy chi ti5t k6 ca phAn biCn d6i O
loi gi6i m6i Uai to6n nhdm tao ra cdch nhin da chiAu, 16 rdng vA c6ch tii5p cdn vd k! thupt kh6m ph6 bdi to6n BDT.
.(r.u.4.fl
: (r+tr+r).f(
a(d +w)+u(S +ua)+c(C +ut)a+b+c a+b+c a3 +b3 +c3 +24abc'\ a+b+c ) > _,,, a+b+c _ \ o+tr-, a+b+c a+b+c ,
cAcn mP cn vA ri ruum ffirlu prr,(nAr m,{l+ nAr il[Nfi THrifl nAr m,{l+ nAr il[Nfi THrifl
HUi'NH DUY THUY(GV THPT Tdng Bqt Hi;, Hodi Nhon, Binh Einh) (GV THPT Tdng Bqt Hi;, Hodi Nhon, Binh Einh) &ii to:in I tth4{) 1: / I r}" {'!t1, 11ti' ',, I.iirr:.
,,1/r,,,,- ;.,. ,rr. r' ( htftt.: t;ut;li t.tt!;,:
.--,.' *_l' _.__ : .. r
t ,;l S/',
"/."' = 1J, ,.' y 1 * Y, ,,I
B6t ding thirc ndy xudt hien trong ki thi tMO 42 ndm 2001 t6 chfc tai M!, bdi to6n ndy do dodn Hdn Qu6c dE nghi. M6t U6t eing thric thflt ld de.pl Dep
kh6ng chi d hinh thfc cria n6 md cdn bdi c6 nhi6u
c6ch ti6p cdn. Tdc gi6 dd tim hi6u vd dua ru 4loi gi6i tti c6c tdi 1i6u hi6n hdnh. Ngodi ra, tdc gi6 cflng tg
dua ra m6t loi gini m6i, ddc l6p v6i 4 ldi gi6i tr6n. Ldi gi,rti I (Vdn dung hdm sri). X6t hdm sd
.t
f (*): -- ' -t r tr€n khoang (01+oo). ta co
/'(r):-.+ .f"(*l=+ +>0. vx>0.Z.\l X - VX- Z.\l X - VX-
Suy ra d6 thi hdm sO 1(x) ldm tr6n(0;+"o).Su dpng b6t Oang thric Jensen ta duoc: Su dpng b6t Oang thric Jensen ta duoc:
a-b-c
,t7 +8b, 'lF.s* 't;'.srb
: o.f ("' + 8bc) + 0.7 (u'z + 8ca) + c.f (c' + 8ab)
a3 +b3 +c3 +24abc
Ldi gidi 2 (Vqn &1ng BDT Chebyshev,. BDTCauchy vd BET Bunyakovslgt).D|t P bdng vO Cauchy vd BET Bunyakovslgt).D|t P bdng vO
trbi oia b6t Cing thr?c cdn chimg minh. Kh6ng
m5t tinh t6ng qu5t, gi6 sir a> b > c.
Sir dpng c6c BDT Chebyshev, Cauchy vi
Bunyakovsky,ta c6'._L_______!- _L_______!- - Jr'+b2 +c2 +6bc tla2 +b'+c2 +6ca c r .( t >!(n+b*c)l : - 3\-- - -/[ rfa, +b, +c2 +6bc 11-)
Ja'+b'+c2 +6ca tla'+b'+c'+6ab )
,-trfu*b+c).
9
1
>)(o+b+cl.
J'
Ldi girti 3 (VQn &1ng BDT Bunyakovslqt). Su dpng BDT BunyakovskY, ta c6:
(a+b+c),=(ffi.w+G;*ffi)
"(oG *zu, +a"[F +uo *r"'[7 *uu)
=( --L----!---g)