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Đề 106 Bài 1: (4 điểm x x x x x x x x − + − ÷ ÷ ÷ ÷ − + − !" #$ Bài 2: (5 điểm%&'()* + , , y x xy y x y x y x y + − − + + = + + + − = %&()* - - . x x x x x x − − + = ÷ + + Bài 3: (3 điểm #/0120345: 6060 0 Bài 4: (2 điểm#/20272.&4860876606, 39: 6;0 6<7 6 Bài 5: (6 điểm)=>8?@ ABC:DB)=>.ECFGC1 )=5G ⊥ ?:H:2AIJ(0JFK2FAL)=>8K2MBJ(.NO0KP ?FAB?:MQM)RHSABT. U?:.?TVWX2EY#0KMWZC/. USGC1C)=>/. J?: 240A[FG'[FK?39. 39Y. Đề 107 Bài 1(4 điểm) - - < - - - - - - - - - x x x A x x x x x + + = − − ÷ ÷ ÷ ÷ + + + − !" A . 01 x A \01. Bài 2(5 điểm) %&'()* - - - 0 7 < 8 0 7 8 0 7 8- + + = + + = + + = %&()* --< - =++++ 8 Bài 3(4 điểm)"](#/01G)*8@0# + + yx x MB#/01G)*. 2027MB#/G)*&407 ≥ 60676ML96067 Bài 4(2 điểm)#/G)*22&4^V'.U 1 5 5 5 5 5 5 ab bc ca a b ab b c bc c a ca + + ≤ + + + + + + Bài 5(5 điểm) )=>8?@ AB)=5GVWZ?P)=>8?H:ABK.E CF_0`1)=5GABDB)=>8?AIJ(0JFaABFAL)= >8?8F2aMBJ(. U .MN MP MA MB= = NbA[F1)=5G#Fa?MBAW. UO)=>CJ(ABO)=>HJ(Fa MQM)RH01)=/VFGC1)=5G. 8,<. + , , 8 + , , 8 8 , , , , , , + A - + x xy y x y x y x y y x y x x x y x y y x y x x y x y y x x y x y y x x y x y x y x y + − − + + = + + + − = − + − + − = ⇔ + + + − = + − − + = ⇔ + + + − = + − = + + + − = ⇔ − + = + + + − = = = ⇔ = − = − 0 c\0'()*Y'8@@ - @ d + + − ÷ ecL≥AB0≥Y x y x x y y ≥ ≥ ⇒ 0 ≥8 60 60 6 60 ≥ 60 60$ 60 60 ec\0≤]0≤ dcL0AB()*)R6060 0 0-0 d0d,⇒)*VWY '01 dcLd0AB()*)Rd060 0 0-0 60d,⇒)*VWY '01 dcL0AB()*)R6060 0 00d dcLd0AB()*)Rd060 0 0d0,⇒0 dcL,0AB()*)R0, fMH)R()*Y-'01820MB8,@,@82d@8d2 .Y860876606,g$860876606-+, $:686087660 6;0 6<7 6 6766060760 680676687606 60 d0767 67 d76< 60 d06 h687606i 680d7 687d 680d ≥ ,.: .352≥ N995&0 0j7, 7d, g$ 0d, 60676, 860876606, $8@0@7@U8@d@d@d]8d@@@ +.Nk90?F⊥K ∆S?T ∆:?F$ OM OK OA OH = $?:.?T?S.?F8 lm∆K?FAWHK1?K ?S.?F8 E8AB8#0:.?T 8VWX$ OA R OK = 8VWXGYT/1?: Y?ST;, , $SU1)=>)=V[?T/. FK?Y)=mAWY1n FK? ?F.K $n39⇔?F39ABK39. 6?F39⇔F_AL: 6K39⇔K⊥?T⇔S_ALT⇔F_AL: aJ?: R R R OK == @KKT - R R R =− c\0n FK? . RR = 8,o.Y ( ) - - - - ,@ - ,2 ,x x x x x+ + = + + > + > ∀ ≥ 21^V':YpMB ( ) ( ) ( ) - - - - - ,2 , - , - x x x x x x x− = − + + ≠ ≥ ⇔ ≠ ⇔ ≤ ≠ ( ) ( ) - - - - < - - - - - - x x x A x x x x x + + ÷ ÷ = − − ÷ ÷ + + + ÷ ÷ − . ( ) ( ) ( ) ( ) < - - - - - - - - x x x A x x x x x x + − − ÷ = − + − ÷ − + + ( ) ( ) ( ) - - - - - - - x x A x x x x x + + ÷ = − + ÷ − + + ( ) - - x A x − = − 8 , - x≤ ≠ ( ) ( ) ( ) - - - - - - - x x x A x x x x − − + − + = = = + − − − cL ,x ≥ 2:MB#/01 - - - ; - - - - x x x x x x = = − = ± ⇔ ⇔ ⇔ = = = 8A x ∈ Z AB ,x ≥ .TY A = .6E8-6067 ( ) - 0 7 < ⇔ + + = 6E8AB8-Y ( ) ( ) - - - - 0 7 0 7 , + + − + + = KJX)*)*)A^)R-8608067867, 6lm60,0AB8-)R7 20AB8)R,@0, NY)R8@0@78,@,@ lm067,2&)*b)R8@078 @,@, lm76,2&)*b)R8@078,@ @, 6c\0'()*1Y-'8@0@78,@,@ @8 @,@,@8,@ @, \90MB'8 cL , <≤ --<--< - - =++++<++++ .a1AW'AL , <≤ cL$ --<--< - - =++++>++++ a1AW'AL$ c\08Y'G09 (GqKr0#/G)*2027.Y6067 ≥ - - xyz KJX)R86067 - ≥ o860676.r]6067$, KJX)R8d<86- ≥ , ⇒ ≥ <.)R%aa<V07 r] + + yx x cLMB#/01G)* 68 06⇔ 8 d0d8 lm-)=R(#SaJE8Y 8 d0d⇒ −=− = y x ⇔ = = y x SaJE8Y 8 d0,2#0 01YV20V ALVMB#/01G)* S-aJ$E82Yj$,AB8jJ 1j≥ ⇔≥ 6$ EY⇒,g d0g d 0≤,.r^B0VW&0 c\0](#/01G)*8@0&4^MB8@AB8V@V ALVMB#/01G)*. .Y + 6 + 868 d - 6 j - 6 86h8d 8 66 6 N 2 (a - b) 0; a,b,c > 0, ≥ 1 2 2 2 (a - b) (a + ab + b ) 0 ≥ n0 ( ) 5 5 2 2 a b a b a b+ ≥ + .r5#&0V. NY ( ) ( ) ( ) 1 1 2 2 5 5 1 ab ab c ab a b ab a b c a b c a b a b ab a b ab ≤ = = = + + + + + + + + + + 88AY )*bY 5 5 a b bc a b c c bc ≤ + + + + 8 5 5 b ca a b c c a ca ≤ + + + + 8- CEAJ8@8@8-Y 1 5 5 5 5 5 5 a b c a b c ab bc ca a b ab b c bc c a ca + + = + + + + ≤ + + + + + + N9st&0V +. YFaF8[9J(0JP )RF:aABFaKuGH. n0 . MA MN MN MP MA MB MN MB = ⇔ = = rFa?MBAW)=m OM ON R= = NbFGbAW?:N2Gb)=>O?ZN2P8GHF. EFAIJ(0JFaABF.Y MN MO ON R= − = 21?aF AWOHa.)*b2?FvAWOH.NYFa?MBAW. KBMWY'A OM R R= > 6YFaABFMBJ(0J8?21Fa?MBCJ()=>)=V[?F. OMBS?F.n0OFw)=>)=V[?F2OMBS. 6Tx OE AB⊥ 2yMB:K8/.Tx 8 HL d⊥ Sz{{?y21SzMB)= ?yF2#0 HL OE= 8VWX. 6NY2VFC18GSMWG^8GCHVWX21SH01)=5 8G|{{8GAB8G|ZH?y. Đề 108 Bài 1(4 điểm): + + − − + − + − + + + + xy x xy xxy xy xxy xy x . !". . < =+ yx F:. Bài 2(5 điểm)%&'()* −=+ −=+ −=+ yzx xzy zyx #/b202734 ,,< =++ zyx AB ,,< =++ zyx U[9C#/2027U,,<. }(Gq&()*# x x x x + = + + − + − . Bài 3(2 điểm)2027$,&46067 %aa x y z y z z x x y + + + + + Bài 4(4 điểm)%&()*'01 0 d d0 08 ](5?02)=58GY()* ( ) ( ) - 0 − + − = 8MB#/.V&E/"CJ)=58GMBML9. Bài 5(5 điểm) )=>8?@ )=V[:K/.SMBCH?K# SKS?.TxGO0NAWYAL:KHS.%"yMBGC13K#y VW_ALABK.a/:ALyPNH~. {U:N :~.:y {[:~.:yjS:.SK• {lA[yV&ESJO)=>HJ( ∆ N~yP9. Đề 109 Bài 1(4 điểm) : x x x x x x x x + − + + ÷ ÷ − + + − AL ,2 x x〉 ≠ !":. U,g:g. Bài 2(5 điểm) %&'()* - - - ; o o , ; o o , ; o o , y x x z y y x z z − + − = − + − = − + − = %&()* - j- 6;j;, Bài 3(2 điểm)%&#f20MB#/G)*&45 ,=+ yx AB0 88 ++= yxP H39.3990. Bài 4(4 điểm) '01()* - 60 - 6<0. #/b223466 U - - - a b c a b c + + ≥ + + Bài 5(6 điểm) . )=>O?2)=V[K .E1J(0J)=> HK2AIJ(0J:8:MBJ(AL)=>.%"SMBJ:M1K2yMB AB:S. yMB:S. [:S• ABV&G?. .AW:KN8 ∠ : ∠ N;, , ABN:K.%"SMBJN1 )=m:ABFMBHS.UKF ⊥ FN 8,.rV≥,@0≥,@.0≠.w0u!")R: yx. ; . < ≤=⇒=+ yx A yx ⇒F:;⇔ ; - ==⇔== yx yx .lr2027≥ .aOAJ€()*ALY −=+ −=+ −=+ -8 8 8 yzx xzy zyx C82828-EAJY ( ) ( ) ( ) , =−−+−−+−− zyx ⇒ =− =− =− z y x ⇒ = = = z y x .fMH90&4.c\007 MB''. E&JY zyxzyx ++ =++ , = ++ −++⇔ zyxzyx ( ) ,= ++ −++ + + ⇔ zyxz zzyx xy yx ( ) ( ) , = ++ ++⇔ zyxzxy yx ( )( )( ) , =+++⇔ zyzxyx ⇔ =+ =+ =+ , , , zy zx yx ⇔ = = = ,,< ,,< ,,< x y z TJM\c\0[9C#/2027U,,< er]62d2dd ⇒ 66d )*8eDB a b c a b c + + = + + •VJZ&OY ( ) ( ) ( ) ,a b b c c a⇔ + + + = ⇒ 6, , ,8 { x x x t m⇔ + + − = ⇔ = ]6, ,x x⇔ − − − = 8AWM[]6, , , x x x x⇔ + − − = ⇔ − = ⇔ = 8MH c\0()*Y'MB, c2027$,Y(GqKrW#/AL#/G)* x y z+ AB y z + )R . . x y z x y z x x y z y z + + + ≥ = = + + 8.)*bY 8 B 8- y x z z x y y v z x z x y + + + ≥ + ≥ + + C86868-)R ( ) x y z x y x x y z x y z P x xy z y z z x x y + + + + + + + ≥ + + ⇒ ≥ + + − = ÷ + + + N9st&0 - x y z ⇔ = = = .c\0 - x y z ⇔ = = = .a\900,MB'. cL20 ≠ ,8g$0 8 do860 8 ⇒ jo(&MB()*#/01. S0 jo ⇔ j o 8 8 ox a x a⇔ − + = o x a x x x a + = ⇒ ⇒ = ⇒ = ± − = 0d2)R0@0d.02)R0@0. c\0()*Y'01MB8,@,@8d@@8d@d@8@@8@ cL"2)=58GVWZ/HC?8,@,. • 2Y)=502GYV&E?J8GMB8. • -2Y)=5d2GYV&E?J8GMB8. • ≠ 2 ≠ -8GPq?02?MQM)RH : ,@ - ÷ − AB K @ , ÷ − . SH?SAWYAL:K2AW:?K2Y ?: 2 ?K - = = − − ( ) ( ) o - + ?S ?: ?K = + = − + − = − + = − + ≥ ÷ . n0 ?S ?S ≤ ⇒ ≤ 8-. E82828-Y%za?SMB 2H)RVAB•V o .TJM\ o . +. {:N :y.:~ . 8 . . 8 2 AD AH AB htl AE AI AH AB AIH ABE = ⇔ = ∆ ∆ uGH {Y:~.:yjS:.SK:N jSN :S 8?:6?S 8 6 - R < ; R {TxN DI D⊥ ≡ PyKVmGBH‚ ⇒ N~y‚CJ(8XY/, , ⇒ )=>HJ( DIE∆ _AL)=>HJ(N~y‚Y)=V[MB~‚ %"TMB~‚ABKN ⇒ TMBO)=>HJ( DIE∆ ⇒ STP9 HK BD⇔ ⊥ K≡ ⇒ TN - - R ⇒ y ∈ 8?@ AL8T@ - - R 8y ∈ 3K)=>O? 8,;.AL ,2 x x〉 ≠ .Y: ( ) ( ) . + − + + − − − − + + = ÷ ÷ − + + − − − + + x x x x x x x x x x x x x x x x x ( ) ( ) . − + = − + + − + + x x x x x x x x AL ,2 x x〉 ≠ MWY:$,.zHY + + > ⇒ < + + x x x x 0:g.c\0,g:g .CEAJ-()*)R86- 6 80d- 687d- ,8 F]V8⇒; do6o0 - ;8 o - +−x $,⇒0$,@)*b$,@7$,. .lm≥-E8-⇒;7 jo7 - do≥,⇒;787j-≥,⇒7≥- )*b0≥ E8⇒07- .lm,gg E8-⇒;7 do7 - jog,⇒;787d-g,⇒7g- E8⇒'()*AW'.c\0'Y'G098-@0-@7- - j- 6;j;,g$- - j; 6ojo,g$- - ; jo6o - d - 6; jo6o8-j - $ - - - - x = = − + + 8 680 68 60 680 6 r]02Y 60 860 j0,j 60 8 60 j80 8,j j d, 6,, TY 6 d,6,8 j6<6,8 d66+8 j 6,8j 6+ n0≥+.r5&0V⇔60 , AB0 E O P C B A H c\039MB+V820 , @ , −+ ] +− , @ , .r]n60@0$^V'Q'Y'MBn ≥8e )*4)*)*ALn - j-n6<n - j-n6<j- 8nj8n 6nd-6-8 lmOfFn 6nj-6860 6860j-06 60 j068606 ( ) ( ) ( ) [ ] , ≥++++− yxyx c\0njABFMB)L#/G)*#/01/-.m)=R(# S = = ⇔ = = ⇔ =+−+ =− - -- y x P S PSS S ] = = y x S = = ⇔ =+−+ =− < + - - P S PSS S AW'AVW&48e. c\0()*Y'01MB8@@8@. cL"#/bY - - 8 8 8 8 8 , x x x x x x x − − = − + + = − + + ≥ ÷ NY - - - - - - 8 8 8 8 a b c a b c a a b b c c+ + − + + = − + − + − - - - 8 8 8 8 8 8 a a b b c c a b c= − + − + − − − − − − − - - - 8 8 8 8 8 8 ,a a b b c c= − − + − − + − − ≥ n0 - - - a b c a b c+ + ≥ + + .S]-8 - - - -8 a b c a b c+ + ≥ + + -8 - - - 8 8 a b c a b c a b c+ + ≥ + + + + OABVAB!")A^Kr! +. Y:S{{K8A:S2K_AWYALK yS S K K ⇒ = 8 zHY:{{?8A:2?_AWYAL:K 1AW:SABK?uGH :S S K K? ⇒ = 8 FBK.K?1:S.yS0yMB:S. Y:S SK.S8 jSS yS.K yS.K :S . K K ⇒ = − ÷ :S.K :S.K . K K − ÷ K .:S 8 .K :S. .:S. ⇒ = − K .:S .K .:S⇒ = − ( ) K .:S .K⇒ + = FB K G = − 1 :S . G G = − %"aMBNS FaMB)= ∆ NS$Fa NABFa{{N FB:K N@:K{{N $Fa:KABFa{{:K$:KFaMBB $:a{{KF.EFa{{:KB:K ⊥ :N$Fa ⊥ :N $aMBbO ∆ :FN$:a ⊥ FNA:a{{KFB:a ⊥ NF$KF ⊥ NF Đề 110 Bài 1(4 điểm) : ( ) yx xyyx : xy yx yx yx + +− − − + − − !": F:≥, Bài 2(5 điểm) 202734'# −=−− −=−− −=−− xzz zyy yxx -<- - - - - - . %&()*#-86+86<86o Bài 3(2 điểm) #/G)*@@3466 ≤ U ,,; <o, a b c ab bc ca + ≥ + + + + Bài 4(3 điểm) %&#f22MBƒ#/b3422≠AB , =++=++ cba cba . U abc cba cba = ++ ++ <<< 39 : 0 7 0 0 7 7 + + + + + AL$,@0$,@7$,AB 0 07 7 + + = Bài 5(6 điểm) :KCJ()=>8?@ .rFC3K."~2T2S •bMBJAWYF1:K@:@K.%"2wMQM)RMB:K@ST. Fw⊥w. MH BC MK AC MI AB =+ :K^.lA[F1KF:6FK6FHML9 Đề 111 Bài 1(4 điểm) Cho biÓu thøc: −+ −++ + −+= a a aaa a aM - a) T×m ®iÒu kiÖn ®Ó cho biÓu thøc M cã nghÜa. b) Chøng minh r»ng biÓu thøc M kh«ng phô thuéc vµo a. Bài 2(5 điểm) %&()* - + + + + < + x x x x x x x x − + − + − = − − + − + %&'()* - - x x y y x x y y + + = + + = Bài 3(4 điểm) K#/@0@7&&' < - =++ zyx .lm60 67 - . .U ≥ 606-7d-„ .39„. Bài 4(5 điểm) f)=>8?2)=V[:KABJ(0JKf)=.1K M902N8UƒKABN.:AB:NMQM)RP)=>HyAB‚@GO0:yAB K‚PHF.S:‚ABKyPHa.U Fa{{K. N‚yCJ()R. Bài 5(2 điểm) Y#/HMQM)RMB<@AB,.[V&EO)= >HJ(JO)=>CJ(. 8,.rT ≠ ≥ ≥ yx y x , , .: yx yxyx : yx yxyx yx + +− + ++ −+ : yxyx yx . yx yxyxxyyx +− + + −−−++ : yxyx xy +− N , ≥ xy 2 , - >+ −=+− y y xyxyx $: , ≥ +− yxyx xy .KJX)*)*'Y - - - 8 8 - - 8 8 8 - < - 8 8 -8 x x y x x y y y z y y z z z x z z x − + = − − − = − − − = − ⇔ − + = − − − = − − + = − aOAJ-()*AL)R 8d80d87d86 806 876 d<8d80d87d ⇔ 8d80d87d [ ] <888 ++++ zyx , ⇔ 8d80d87d,. ⇔ ]0]7 cL]0]70AB')R07. c\0AL0734'4. %&()*#-86+86<86o g$;86+86<86o [...]... AC AI BI AK + KC AI AK + = + = + MI MK MI MK MI MK (1) BI KC ã ã = ) MBI = cotgMCK MI MK AI CH à à à à = Do C1 = A1 nên cotgA1 = cotgC 1 ( 2) MI MH AK BH à à à à = (3) A 2 = B1 nên cotgA 2 = cotgB1 MK MH AB AC CH BH BC + = + = c) T (1),(2) v (3) suy ra MI MK MH MH MH Gi D l giao im ca MA vi BD ta cú : ã ã ( Do MBI = MCK cotg BMA MBD ã ã MAC ( BMD = AMC, ãDBM = CAM ã ) MB BD = MA AC MC CD MB... giỏc ni tip 5 a) Ta cú: BC2 = AB2 + AC2 102 = 62 + 82 A O r 10 0 I r E 8 C ABC vuụng ti A, nờn trung im O ca cnh huyn BC l tõm ca ng trũn ngoi tip tam giỏc ABC Gi I l tõm ng trũn ni tip tam giỏc ABC, D, E, F l cỏc tip im ca ng trũn ni tip (I) trờn cỏc cnh BC, AC, AB, S, p, r ln lt l din tớch, na chu vi, bỏn kớnh ng trũn ni tip tam giỏc ABC, ta cú: 6.8 6 + 8 + 10 = r r = 2 S = pr 2 2 Theo tớnh cht... P b P c b c a 1 1 4 + P a P b c P P P 1 1 P P P 1 1 2 1 1 + + 2P + + ữ + + ( a + b +c ) + + ữ ( 1 +1 +1) =9 P a P b P c a b c P a P b P c a b c (p dng Bunhacopski) Du bng xy ra a2 = b2 = c2 a = b = c 114 Bi 1: (4 im) x 6 1 10 x + Cho biu thc: A = ữ: x 2 + ữ x +2 x +2 x x 4 x 3 x 6 1 Rỳt gn biu thc A 2 Tỡm x sao cho A < 2 Bi 2: (5 im) 1 1 9 x + y + x + y = 2 a) Gii h phng trỡnh:... cung BC Tng t ta cú : a 0 (111)1 Điều kiện: a > 1 a + 1 1 a 2 + 3 a + 1 2a + 2a a 2 1 a 2 + 3 a + 1 2a M = a +1 + 2 a ữ= ữ ữ ữ a a a +1 a +1 Kết luận: biểu thức M không phụ thuộc vào a 2 a) Chia c t v mu ca hai phõn thc cho x v t bin ph b) iu kin y 0 2 1 x 1 x x + 2 + = 3 x + = 3 + (1) y y y y 2 x+ ữ= ữ 3 a +1 =3 a +1 a a 1 x 1 x + =3 x + 3= y y y y 2 (2) 1 1 . MCK ⇒ · · cotg MBI = cotgMCK ⇒ MK KC MI BI = N µ µ µ µ 1 1 1 1 C = A nªn cotgA = cotgC ⇒ MH CH MI AI = 8 µ µ µ µ 2 1 2 1 A = B nªn cotgA = cotgB ⇒ (3) AK. 240A[FG'[FK?39. 39Y. Đề 107 Bài 1(4 điểm) - - < - - - - - - - - - x x x A x x x x x . OE= 8VWX. 6NY2VFC18GSMWG^8GCHVWX21SH01)=5 8G|{{8GAB8G|ZH?y. Đề 108 Bài 1(4 điểm): + + − − + − + − + + + + xy x xy xxy xy xxy xy x .
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