Những viên kim cương trong bất đẳng thức Toán Học Phần 2

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Những viên kim cương trong bất đẳng thức Toán Học  Phần 2

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IV: Chlrrrlzg rién /cim clrrmg Irong 1\‘l117'ng I211! (hing I/1121' §1s PHU'()'NG PIIAP DON BIBN tét T6111 II 5-19 11111 (MIXING VARIABLE) dung: n51 11511 1-511 /zifn 114% B511d5111g1h11'c 11:1 111611 \0'i @111" 111 11111 1111 gi1111"1 1115111151 \11'11g 1.B1§1d1'111g1l11'1'c 1\'11511g 111151110511 Z D511 bién D511 111511 111'5'11g III D511 IV B211 111'111g 111110 v v11.1)611 bién 111111111f.\~1v> 11i.\1'1\'1 11151113111) 111511 11'0ng111n1 gizic 11-1e11 11611 1111-i~11 111j1¢ 111111 15ng D11111 1)‘ 11511 111511 XIII 111é11 115111 1111111 101111 1111511 \'0'i \11f~1 XII 116111 111611 1111 111511\"§g11111'111"u11g1111111 EMV \'0‘i X1 d11'5'c c1_1'c 111 11111 h§11g11Z1111 151 bién bng quy D511 E.\11V Z g111c 111111 B5111.111g1111'1~1~ 111é11 11-11111111 1111 VIII D5n D511 11'011g bién \'0'i 1111 s.\1\1> VI D5n hién X gizic 111511 b§111g 1\'§111uf1111Z1111 911111 1y IX kién \/0'1 1151 112'11g 1h1'1'c 00111511 \Ih111 \*1‘1 11511 1111 (G.\IV1 1111111 15p DAT VAN DE ' C1ic 1117111‘ c1ic'b111 1h1"1n diing mén kinh d11 1111511 111111‘ c1'111c111'111g 111 x1'mg h11y hon 1151 1111'1'c nhuu M51 vi 1r011g 111511 111 11111 d€111g1h1'1‘c s1111xé1y1"11c1é1ng1h11'c Bi1i 1.1 C110 1- ° S5 1u'5'11g c11c 11111'c $111 xziy 15111 1'11 11Z1)' c0 dy B511 11111111 111 11151 1111 211 Khi 111é 111511;; c110 vid1_11i€u T1‘011g b€11d1-“Ing C0 C15/111g \'i1c111'k11i \*= \1 \*i{.>c 111101‘ 1101 1111'1'c 111111 ‘\'= : b51 dzing xz1y chng 1h1'1'c 11510 11151 Ia c1ic bién $5 bng hgn \1'0'i /1 : 111 1-_ C0 11511 (1: 15111 Q0 101111 1111111 111% Q6 \a_\' c111111g 121111 111 11151 111 diéu 1u511 1i11 ring 111511 11111611 _\".;e 21.1-’+_1»1 + 1111'1'c 1111)-' 1111 c1?111 -P X61 x1"1)' 111111; 11151 11:11 11§111g 111111‘ 1151 x1'1'11g hién $5 1\'11511g 1'11 151 11311; 111111 11151 1111111 C15 1'51 c1111_\511 =9.1.('2() Chung minh ing: _k_ Q - -'+~!l~+~?Đ%\1Â1+/v+ 31> 1' vi) (‘zic han c(v1]1C' hiét mil liun chm déng lhirc xay ru =()(\'Z1c;'1_c dang hozin c6 gi O) dzfac nhu" diéu dfxc biét G6 121 thuc khéng fun nén bién hing 1Z1 hing c6 mél bién () ciwn du‘‘c Vi gia goi bién IE1 vi nfra 151 czic ban sé cbn gp nhfrng bait dfing lhirc mil du "='" xny nhiéu h0'n mét Chg (khéng tfnh czic hozin vi) Chdng déu 151 czic bnl ding lhirc dqp vii kh('>_ chng hgm nhu'm1 bin lozin rl n6i liéng sau dy: ° ~M©t diéu thL'1 T Bili 1.4 (Iran TST 1996) Cho i Phu'0'ng phzip dén bién duqc dél ru dé gizii quyél czic Bing xay tln1"6>'11g 111 lhco V + Tru'C>'ng hqp tét cé czic bién $5 bng la sc + Truimg "=" du'Q'c du'\‘.:) 2/ (/.I.I) f(.\'.>\".:)—‘/'(I.1.:):.\"+_\‘+:—3 Q/.\_w": —§ Bu'6'c 2: Chung mmh _/(1.1.:)= 21+ Thé1t\=c_1y _\~ _\< 1: N/Ty ; Tu > Q6: Z1 S \'+ _\- suy 1'11: 2/+:—3~{/.\1\":J:.\~+_\~—212() ‘ -3-"\/I"; 20 " lucéi _/'(1.z.:)2() 20 v \'é'i (Z1+;)' -2711-_2(1(1—_-A):(8r+;)2() (dung) Kétluzfm: _/(1-.v\~.:_)2/"(/.1.;)z0 Crich 3: Bu'6'c 1: K)’ Néu lhuz_31l chuén héu lhco tfmg d6i \'+_\‘+:=/\'>O thi(l)(_\'+>\'+:)‘2Z7.\1\': k} lhuql chmh dung dc don hm blen C(ich1.‘(1) _/'(.\"._\"_:):.\"+_\’+:—3-{.\j\‘: *V_\"._\*.:>() Bu'0'c 1: Chung mlnh: ‘/ (.\‘.>\'.:)2 [rung dgai lm_)'ng Ch 12'/lg I1 , I lix llmu hién hui l\Lrb'c ll‘L1‘O'c xél m (), _\" I xi Ihi diéu kién déng {hire 20‘ ' nén ta Chl phai xcm xél su lhuy déi cu;1_\"+_\'+ t Theo = \‘ \" , 1) A ' (*).khid(1(1) Q =1 \ » \' ~ Q \ hm) man urc du'(_v'c Bu'6"c3:Thav:=1—21u1c6:f(r_r.:):1—27z3(1—21)=(l—6z)(l~3r)' V0‘1Cl1eu k1¢n("-‘)lh1CIangLhu‘c 20 Z7.\‘_\": Thco \-_\': Q» _f(.\- II _/‘ (_\" _\" {hay déi cuu SL_l' , :1‘ , \\ dé :> (dpcm) 1' Q 2f:-1‘ Q \"= 6 hi 1hu)§1 phuc h0"i minh \"1'dg1 tI111'z~ don gian nén pl1u'=2(z1+1)l Dc dimg chung mmh _g>(11)2()bang kl1:10s1i1l1Z1m Lhco bién D€inglhL'1‘c xay ru vil chi 11:/1:010 11 : Gidi NĐul2+1*;Â() chun lwglc :>_r'11.1.1->21ằ \'Z1ch1 khi11=/2 111$! 1hL'1 hit dng qu;i1_ —9("_1 —1811~+(21‘ —13+8).T;1c(>: Bili 2.3 [Viét Nam TST 1996] Khéng giéunti11l11611g * ,_ . \ +-l(\/11+\/w) Â/201111)" _/'(11./>_1")2 _/'(\11/a J11/2.1) \/Đ1)'bi1iI0z'1n chL'1'ngminhxong D;'1ngIhL'1'c xa); ' nén chi cn 1" 1/=_/'(.(')—‘/’(\/_1",)—(\'11~\/w) ;_2(\11+\/>1 A'=(91)’ -(11 +2)' (21‘ -11 +14):-(11 -1): dévn /1 11 kh(mg m = (11: + 2)(/7: + 2)(1': + 2) —9(11/1+/¢1'+1'(13 \' @511 chL'1'ng 1:/%5 minh: +6/n'+u : —>u(/>+)2() , , Git! sir u = min{u./2.0} :> Z/>3 + 20: +8/7('+u: —5(1('l>+¢') = I/73 + Z0: +3/70-411: +5(/7~u)(—(')1 +\///2+(('—u): I (1 +/1 +0 = Chfrng minh +\f('+((l—/7): \/J3 ring: ‘ { C/'11?'ng D31 VT = f(_u./2.0) Gi2'1 sir :1 = {(1.110} minh D0 41+/>+ 111 Q6 \'Z1i 11111111 suy >111z1.x{ O x61 dé 111 1h0z1n1Z1111111111c_>i /1" g1:111 111111 /1 >0 > /1 111311 11511 101111 cf111g1hQz1n1Z111 vi: 1111+/1 1h1 caic 1h0z1111f111 111é1111 115 101111 11211 suu 151 111'1'\'11g d11"o*11g: (i) (1)d1'111g (ii) (1)d1'111g 161 111111 11./1.~: [3l@111gll11'1'c chtrng minh dL1\_)'C It I \Z1 Â/ xilo /M/././1\ J \'Ief1Ikhzic.lI1u\' +/n'+m)E ,(u+/1)‘ Tu)" nhién nilu czic ban thu' dén bién thco czic rt phirc tap Bili 2.9 I K 2% “* {rung binh thi czic ban [1100 sé thy viéc nily diéu kicfrn I + 3a/2r‘ 1" C11/rug minlz Dill + l K/>+'11g 1f\i cht'rng minh kl1(mg khzic hil gi xu \"O'i hl dflng lln'1'c dgli \(‘\ nén 0' d[1§ chx xin néu ru Ina}! \‘L1i \*1'd1_1 dé minh hQL1L‘l1U \"(rc mqnh C1111 phuvng pluip {rung dung ht dfmg um nix} Clzing Bi1i2.l0.ChoAABC l‘imgi;iu‘i ‘I +1-0.\:¢\)(l + 1xhonl1f/atclux: (l)df1ngl1u)' _/'(‘~\.B.C)2_/'(ii;[i.iJ§'5.(‘)= §’(C') : i’(3—r'0\C): (1+z@.|-,1 \(3'i 4 Béng lhirc xay 111 AABC déu V5)’ _/‘ :1(;_f Bf1i2.l1 Cho lam gifxc ABC kh (‘~\)Z)' (/>+1 +2 tri Iéch 2- ding thtrc = = nhung sai véi 0;“ +11 + ab > 0, bit déng thtrc sau Citing £k\/a+b+c+d (1 \/(l+a C 2+, 1> ba girl /'i cua czic du lc'>'n hon nho h0n_ vim C6 thé tim dtrqc nhftng (mg dung tronu\ céc biti tozin thttc té D6 lit nhfma\_ tu' ttrcmtl\_ - ttic cét vé triét dé 1)?" V51 thuyét thtrc hitnh ctta nhiéu tzic gin Czic tn" ttnmg v21 nhfrna tim tbi rt nhiém C t_/ fay da du"Q'c phzit trién m{)t czich cfmg nhb dé né trv thitnh nhfrng phtrong phzip dcp dé nht hién Chting téi hi vqng ring tinh thin sng tgto ty sé Chrqc czic ban tiép tttc vit phzit trién nhfrng ting cao Trong Tozin hQc khéng chi c6 riéng b§t ding tht'rc nhung dé c6 thé hbc vii litm tozin tét thi tinh thin szing tz_1o IE1 yéu t6 khéng thé thiéu Mét mong m('>i lc'>'n cua chting téi bait tay tht_1'c hién cuén séch nity lit phrii litm suo xy dung du'Q'c mét cuén ttr dién tit bit ding thtrc SO‘ cftp ditnh cho cit czic déi ttrcyng ban doc Quit thtrc chting téi d c6 gftng hét strc dé thé hién duqc tm nguyén 66 trén ttrng trang saich Nhtrng qua théri gian chting téi nhém thy viéc truyén dtrqc cam himg szing tz_1o vit tinh thzxtn hqc tép tozin hc tdi czic ban déc gift i kién thirc hay mfn k§' nfmg phuc VU cho mét cuéc thi n210 dé" khfic vdi hqc sinh nu'é'c ngoiii viii ciuzg mot don v_i rhoi gian ngoai viéc ti_r hoc chuyén sziu m6n hqc yéu ihich hq cén duqc nm bit nhiéu kién thirc ky néng bd {ch Lhiél thirc vii gin gfli vdi cuéc sdng Phdi chfmg vdi cac hoe sinlz gioi chfing ta khfmg nén day hqc 10 h(_>c cho hQc luyén thi Tozin qudc who gl.()lkl'é’l1I/1llZ‘”, cho van ba ban toén dé hc sinh nghi gin hét buéi hc_>c r61 chfra mil nén day hqc thco "nhu cziu n kién mm czia h_0c sinh” vdi phuong thirc ddi thoai cdi md: "Trao toim bf) théng iin_ 121i iiéu cho hqc sinh V51 hudng din hqc sinh czich tiép cén, xii 1)? théng tin rdi czich mt; réng dé caich l2_10 czic vein dé mdi" Nhén ihirc [£1 nhu‘ vgiy nhimg viéc bién thfinh hanh déng lgi lién quan lruc iiép dén 11161 sir kién dd iii chuyén viéng thém cua Tdng thdng /VI] Bill Clinton sang thém Viél Nam iii‘ 16/11/2000 dén 20/11/2000 Téc giél d iheo kiéu d6i thco sci‘ hién dién Qua Tdng méng My aén thém Vén Miéu Qudc Tu Giém, gép g6" thin thién vé'i ngudi dim H51 Ni tai khu phd c6 buén bzin Hiing D510 vii déc biét viao lc 16h I7/11/2000 gap g6" vdi czic giang vién vii sinh vién DH QGHN Tdng lhdng d5 phat biéu: “We cannot change the past What we can change is the future” tam dich 151: “Chzing ta khéng thé thay ddi du'_ac qua khli; czii ma chzing ta thay ddi la tirmzg lai” Chinh céu néi d lam téc giél rt cudn seich gidi thiéu nén Tozin hc ph111 11131 1>1é11 111311 011n 1111115511 111311 1111 1-1 W111 vién 06 111 "0ng r'1y diéu ng11'6'1 1111-Q-Q! 151)’ d11'0‘0 6111 1301 15111111611 néu 1111 v0'11'6! 06 111 1h1 k16n'11h11'11g xc 1111 phrii gid dd!" 111111 1é @110 1h1"1y dén 11160 11611 d¢p Q dily diéu kién an-qc vq n-1; ch11'11 1161 11151 10:11 0110 1116 11'é_ d6 b6 kh6ng 06 0611 vi néu dy 1111 11161 1111511 1511 sém C1111 1'11 111 v1 ngu'6'1 dim 6ng m('1t tlzugic tinh gid 66 1:1 aiéu v0ng 1111311 0110 ma "gm" 11161 1111 11z'1n1 1111111 06 don) 11111131 111111 11111)’ 111611 011ung kh6ng 1hé 1510 616 kh6ng ph1'1i 1111 " Cz'1u chuy1§11 1h1'1' hz11 11161 111 Q6 gzii hz_:1n 15111 gap 11gi1_\J dén nh 11161 161 1:11 cimg gia Q11 11‘11'u dinh Khi 116 161 1161: "f)u'()'c r5i nlurng 111.514 Irrii m1ra'i nhgin dinh niiy di dqc qua hon 1000 trang cuén szich F121)" .\/[Z10 clii c6 thé néi dy 1?: cuén szich viét rt céng pbu vii chi liél giéi lhiéu czic phu‘o'ng phiip déc séc nhzil chirng minh bail dzing thL'1''c VTV phzil séng mél $6 sgr kién I611 Bili hail du'Q'c ;\"zi11g uic H1351)‘ 29/7/2007 dé chilo mtrng IMO 48 dién Ihnh céng tél dcp Bixi hfu du'Q‘c léng duyél lflc 1lh()0 ngily 30/7/2007 vil dlrqc BTC chqn lilm bi hail chfnh lhfrc Irong lé bé mac IMO 48 Nguy mu dé biii hail d du'(_>"c Yang \-‘ho khoanh khc cuéi cimg lL'1c 18h201r0ng 15 bé mac IMO 48 du'Q'c VTVI 1TLl}’éI1 hinh Iruc tiép t2_1i TT H61 nghi Quéc gia 121 FLAME OF IMO iii“- Music : '|"R-\,\ Pm 0\(; Word: Truong Dieu Linh Bzxlladcl J nu) L- T F‘ ~—r ' Q1‘ if - - /1_\ [$4111 [.143 \11/1' \u’1'v 1111111 011 - 1'1‘ 111 3411’ I7 , a he - l1cf/ 111131 ' ĐrffĐ,'Â1:1'5'r'E 11,1, I/111/1 1"1111_q EV Y\ W E1‘ -5 \11/0 1\ _ 1, l p %§d’f4'4‘ LI C I ,\I U /111/1/.\ 11.\ 111 I M L17! 111/1 1'/1111 1g V»- .\/ - gel/101' ‘I I11 /11 /1111/ce 11.\ 11/ 1/1" ’ 1/11' '1llg Iu /11' 011 \ /10/u'.\‘ 1111 U /(151 1101 11' 11111 _-§ ‘/11‘111 u'11_\".\" 11m/

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