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a Hal to > ab rbe toca ®O
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ay Sự tu) Ni xauz 2 vƒ+v ` »o ney
Pe 3x+dÐ + TH les + (At £G)| + (rry)
Số Am bất đáng TÂM» AM- GN va gia that x+y > % da Ake
Plạ 8 + 20) tần = JO Vay GTN ova P= 40 Ws n= 3, y= 0
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Trang 2rổ > + @ TÂN < Rất Aa Mia b bf ch (21 ob LAL | | + xr+S +2 aa [ z#+5 tut+2 > Axrty+h aS a @ -(Š + +2~)+ AP +y) + 3G4ry) Ap Àu ch ot De Ax 2\Š.x 222 By + Sts 24+A.51+21- 33 ey NA can cao he ai far x.y > O ve xu + 4< 20.Tùo GÌNN ca A< XE 2V— " >on es n+ > eg - ate » dự it Ỏ Các) 1 : Lt HH Hit k Ke 2 = z4 aco: A= 2041+ - |1 — No Ai hoa Dat = >t? | + +>T?<)† a
+ ¿2124 _ 1 ¡ó1 Bd
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Này 27NN cứ Ra Đn Veh gad, y= At
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lu vz@ > ais bie > 2a bre ® + >
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c`+ arr » 2c\a+b ©
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= Az Iuu + ty ty = HT t3 “Ma Tổ? ?hp
ee ee _ |
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Nz&zo &+ 2z)(c+ 24) V(c+2b)(a+ 2b)
Sử Tự eat az, ony due AN- GM teed:
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Trang 4
man 22 be
Bai 8 Nebaib< dic diay dhea au ab , be , oo = 2.Tw GINN ca bids ue:
T= arbye4 1S
atbre S“ day ak 422) Rb AM- GN tac: 4 db, be), 2l a 1 a& be _ c a Lert) > TER << A ca alo Ca IS)? ya ea Cầu: đc ve! > bey & > arbre > O<a+b+c< 2 pst œ=a+yb+c© > OcR4S qt ne Ae yw Ocxned Thcd: T= 4a( 4 +) - 4x The WPT AM-@M và oc ned địa cá - Te X3 29 { [| il vẻ AB + 8n = na .cann Chel) 2]
Vasa T-(x+#)+ A Thee KĐT AM- @M và 6< z 43 đaco: ~ L
1» 2 RA + + = 22 Daa lh 7 n= a,bh ds a-b-c-1
0 9 TT _|2?_ L 7 tele
Vay GIN oe T= 22 }ka<b<e =+L
Poai 9 Che 2.y)2 70 hóa vào ory + #T 4 ay Tan GINN cua bidy 48zm| = A + at + -3
Lab err Gray (E+ 3)"
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yio * raihi fiz a? 2 GIG — 24 S
Piette! [eae ~ fees Ji lại
(@+2) § § T (+z)-€ § 2)
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abe arb+c ab “be 7 ea * a+E+c”
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Trang 5'w@,@ wš ® > tr x.à—» S2) — (ab +be + ca) ® Theo BHTAN-GN: _A + 3(a+k+¿) z 6 a+Vxc*# > 1 œ+b+c*~ >»6- 3(+b+c) ©) TwWAwOs> x 6Ð - 3+ +) - Rifle + be + œ)
<=> Pr 60- 2(a b+ dab + 2be tea) — 63 (ab tbe red
S Pe sÓ- 2(a+b©tc) ~ 21.%.(ak+bc +) = B1- 21 %(2b+ bc + ca)
Jac: (&+k+”“ Bab tbe HPF a + +~c°~ia —bc — ca Leb d(b-oL (a 20 > —3(ab the+ ca) > -L(d+b+cÐ = =1 2m sktstcteb eH >> SI-2I tết co)» SỊ -l2Il = Vay, GININ cua ‘P= 30 Mh a= bee =4 Cade Sé ding BOT AN-GN te cd: aborbe+ca Tapeh ate %3laL.k.œ« = 9abc — >5 al} [a 1 > > = + 7 R: _ | lst
Pe ia a++c*“ "Tư aie Ul i (at on +
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ale + be tea ot bc Cte a*+ tc
par y= athe don bel %_—Ì - @-Ð tơ=S c€2) xo > eed
abibetce 2( alo c+œ) "|
Ta aitec Pei IS 49x 4 = Ad + 2(~+‡+) +9n = 19 tafe +@ED |= 20
\lay GNN ote P = 30 bhi a-b-c= Cad
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rit tt 8 y t R+y+t © Da =o bin=y-2
OF 41 _ atbiC ol} | aaj} td 5.5, HE J
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> Sat aba \a+ TA xbc kea Perera s@b tbc +a)
Jac: G@+bic) Bab tbe hae II Ted’ —|lale “tees
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— >> %(ab+ke+ø -(@+bt+c) =1 @
Ap Aury © và @,lf ® > К_ 3+ 4L - 4121-4O
(@x+kx+‹Ý“ 4
\ ay GINN o& P = 50 Whi a-b-c=4
Trang 6Bai l2.Cho abc eo, a+2b64+3c=1.Tim GTLN, GINN cia bit thie Pez f†? 1? < Che Than ta NS 20223» HD Te g@ thab > Oc a <1, @<b<« HW! @delel Aco! os at ia ` ``\ +P< +(Œ- Se\re 2 Oo < 2$ 28 (vw ofc & ).Ð.4 Pe =O okt Dar s \ Thu ccna oy Atrebt+be = 4a44b+ 4c Pere 28 lhio- 4, be 2, c=0
x Jaw: =§&+6b+6c)(a+k+‹)= 47+ 6b + 6c + 3ab+12ke + Fea
TP: - a°+ 4k*~+ ac”+ 4a + 12bc + &cø > 3P - Sa“ + gle tABcr + lab + 26be + ca
2 = 2a + 9Lk”7+cYt§okb + 2 bc + 12 ca
>9P- 2 - a?+4okFt1sabrlzkerdcazœ > = 2 Wiab,czo)
Dat =lch Wht a bl= 0,0 = +
Vay GTNN cus P= 2 = lÌ› Ta cat
Bat IS Choa ber thia min ath > 4 Tim GINN cáa bữa thie: P-= 6fWae+) + Š - 3 < Chusin Toon tt Giong 20237 Hp zu v + acd: Qa +b) = @rbd+@ b> @rby + 2(a“tk) xÌa+b\ š a+b > Pz Elarb>+ AG 1 -3 = 16 + @rb| 4+ 5(arb)-% a+b a+ Si ang BST AM- GM Na gis gót arb >4 > P > 2he +S.4-3 = 95 GANN cua P= 95 bhi a-b- 2 TT
Poa 44 Cho ajc > 0, axb+c=4 Ching sella ig:
T a(sb‹ + )Đ”~ b(aca +1) ott sab i]
P= eortty + ata ti) | ~ Babes) ? I~
< Chuo Toa Las Cai 2023> HD 4Ð „- dbet\ ys cael SabtA LPL +7, ,# Cc SH dug BET At GM td: emp > yo C— ae 24 z > + l6 =" 72 TP St tr? r®t 9 a, R 2 hz
et? > Pờzx+au+#
Talc! Ktyrt = 3b++ paced Ca dart = (+34) + ( + 2b) +#+9ð- €(fa+L+©
Se Dung POT AM-GN >
%+9++ +23 x29 +2Á4-6 - 12 > PZIZ
Trang 7Dai IS Cho các 36 ture dong Lips thea wan J1+2>3 +2x+2) +2# =5 a) CMR: A + 1 2 mm ¬ L) Tim GIWN o&% P= Xt , Yt , 2tr4 a7 tl 2y +| Az4 <ChuyjSo Toom TPHCM 202.3 > ay Qi lận BOTAM-GN fod: 4, J 2 lũ kien 3 @x+0@01+1) z ® @ 5 + tực Wy z= @ QE +N 3 VW ga Wak ta ch: Äzx+0(2u + + “hi Tra w( 4 A be = Ae 1) + 22 +Ð] > 4 Vex Daytt ae th A 3 > x = 34 Ê at + Âx:jGaS 2t 5 2 ^ + Dar = voy rchhi b0 tÒ =2 z =4 by Tac Po AH, Yt, ere 2+1 2y +| Ata 2P 2a ht ee 2x +1 31! 2z+1 2z +\ A + Ae Ar 1% 4+ z+l +4 > 2P- SS 6 + mm) “li SF dag BAT AM GM Vay ) ta + ứ = a cô: ar | 2 2 h _ 2P >3 On + D(2y +1 TT ?F 5 Ee Pe A 9 _ 1» li _ 7 i
Mẫu 0N của P= Mix <a=t z1
Pai 16 Che a,b,c Eat soto Wt al Dan 1 CNR:
vob 11 |_ , Mec=1 ea a+xb+c b+c cra vr T 4 < Sr Toan Can The 202 3> 5 eo Si dig BE 1 AM- IM sa os: {đaE-\ „ Vab _ A — { =-4- A a=-L) bre | ae 2 be J <( b A fA aW Aa: >, fab-l„ a 4 ft ? bac + ale b @ Vuong WR tac Vbc-l\ „ A (A A md caa Ft Ala c @ cas} fo Af a tae arb 47 als L) ®
Cong thee se O,O.8 > dpom Dar = olia-b-c= (2
Pai It Cho asc >, ab +b} +! cd =1 Tm GILN ca bith thre:
H- 2a + b + —&
— Ä4x~aF— lIx+b” JA+c"
a+ ab tbe +o = (at+byatc’ } 41+k~= V+ak+b©c+œ =(a+by& +c)
Trang 8re > 2H < 2+2++- 2 Snes as+bc+ca=1 bà TT 2k L 1 (is arb TL TP c ˆ bec fe Lda art 2b+e) we OD tt! biel | i \Jay GTLN one i na = b c TC Pai 18.Cho ad, Pp: pete GIUN wa Lier thr: & b q tr Tat "orb * fare HD ee Atay =a + alt +bex+ca=( x+bESCa + c3, 1+E =Q+c)(ax+k)› Aten (bi d(c+a) “Ja duce 3b 3c
aH= 2 's+ư€ {Vern ab 2 Vale BG
Stag S wa leis an on hes 3b 1n “r† ate a+b ie 7 it Pate |= Trʆ 3 & >t 4 + (Dw = x án ha LÀ Boa = ^^ _ 3a si a iz 2 = = — arb te) > | 3 —= = L = C= Ao T Min (2S ab | betea = t œ H- AD -| At ~ LAL
Nay GTLN om R= Oth a = Fe; 2c = te
Bai 19 Cho a,b,c Pur “thea wan (a+) (b Her) = (a- \(b-1)(e-1)
Tim GTNN co A - lal + \bl + Je}
< fe Tin Ha NG 2023)
Tat gid Shick O+DCb+Dlgrd =(a-Nb-N(e-1) & abtbercas-1 O Tad: A = ee alglele te) = = a+b 4+ co + | ab| + bc} + Ica!)
arab tet Lobrbe+ a) +2 + 2(leb\ + Jbc\ + Ical)
@rb+ + 2+2\obtberaal > OF24+21-=4 SASLZ (wWAZOD
le hay an asl, b=t,c=0
Ny GTNIN ofa A= 2 dda chaty than a = 4,bkljcco
Bai 20 Oh a ble >O, ax 2b + ac - 2 CMR _ „| 2ab +HẴˆh—-+hÀ—-k>~ = VW22E: + 2bc+a ac+?Ùb 2 HD Dat xnaard,y=d >0, E-48ce>0 SxtyteE=3 i x ye | EX TF My + 3% fF yer Sx * EZRHS
Teta dc: 20 + HT CP oe Y=(U4 2) (+E + aie — FY) (x+2), 2% r3y = (x+ylys z BX=@ >)
Trang 9Bai 21 Cho xy) % >©, Ay ey +4 < Gy Tun GUNN) cite: M = g 16 x— án a (2+3)— "Grae (E41) ~ <Thi voo 10 Thanh, Hoa 2023> HD Sit dug BET AN-GM ford: 6u FIA eo AOI + (yb) + ACE HD > BX +BY + RE > 12 >z4x+u++2z @ g = + K+S + R+3 > => Zz @
(oc-+3) 8 $ +“
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dept etre tial
Cory dus ve, © © sw ra N > 2026 +3 — L(x ryt Ae) y 2006 - 3 4 yp - ae Pe
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La qu Asan; eet AN-GM ae Aduale ki của ae
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Tug Ns 2 yg ye yr ~ 2
x _ xz
1L Z z2
® xŒœ-+w+>)- + (xu tuz+ zr) = 3~— 4 (ey ryt + te)
Lại cai (REYt tỳ 3Jr#+z2) = +@œ-vŸ + +- y+ 4@-2)"> eo
> ~+ ry ryt +t) >¬+@x9 xx+) cổ > AQ» dial 2 =
Trang 10Pai 2 Cho cas $6! Hue aw abe hse ma arbre - 3 CMR Qe a+ ob tr + c+ Ja 2 4 chs Thea _ a(a+ 2b 2b) _ Pate 2ab~ _ ab” EF - a+2E” ñ a+xzE a+ bˆ+L~ Se ĐỜI AM- ti OF ¬ > |_| 2 Yar ak © Sg? Oo aa Oe [ting AS tf: bt2cr 7 bY b-k c~ z C— + chan c+2a*“ 5 > pyas- Pe arbre 2 (Nai We + Neat) = 3- = Clot Bot + Wcta®) TA EIEìN Aa 4 Wer + “jcah 4 3 ar hott zZ atktab “| 3 ® ber zt bactbhe 3& = 2 crater Cong thes ve > © £Fabro+t Gbib.ta)= 24+ 4lob the+ ca) lđ) Cs: @+b+‹3 ~3(ab+bc+eO = 1@-)T+ ?ứ-ở++(-sŠ > O >> eb +bc +a) 4 %(& +tb+9ˆ= + TO EO > > HAS aig ails Gok sb Gs @® As