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! "" " = − − − − − ÷ ÷ ÷ ÷ ÷ #$%%&'()&*+%,-./0'/1% 2 - - − = − 3&'()&*+ 41&$'(5&6&'()%,0'/1%78-9:- ;0-;%%'6%"∀- ∈<=8=0=%∈<9=#%%>?=0=%.@%'6%" 41&$'.1%- ; -;2A&%B&'>$ 41&$'(5&6%BCD*E?05& "" " = = = # "" "" " " + + + = ÷ + + + 4%%.1%:-*FG-* H-F IJ:* ;F 41&$'(5&6-G*GF:"#KLJML'.1%.?' ! N'=O=PMQMRSML(&.'/$%%%TJ4=4=J%,∆J4UV&L' ∆J4KW%%.TX&PYKLO%PYK&&B%KL05&P=OK&&B%KL 05&O 41&$'(5&IO;O;P;PY:J;4 Z∆YPKL∆O 41&$'∆YML$&'%K&%[ " #$&'()M\]%,0'/1% - ^- " J - - + + = + + !"#$% &'(! #$%& ! "" " = − − − − − ÷ ÷ ÷ ÷ ÷ ""_ "" ""_"" ! "" " !""" − − − − − = × × ××× × = " = '()*+,-. 8 9 8 9 8 9 ! ! − − − − − = − − − − = = ÷ ÷ ÷ ÷ 8`9 (#)%B 2 - 8- 9 - - - − − − = = = − − − − /3&'()&*+#Va'%B - − ∈<⇔ ⋮8-G9⇔-G∈b8 9 c#b8 9:d±I± e=+M3V0X& -H H H - H 2 H! 8a$D9 8a$D9 H 8a$D9 " 8a$D9 c3*K\'-∈dHII I2e#3&'()&*+ (#)c#-∈<+./3&'()&*+#Va'%B 82G-9⋮8-G9⇒82G-;-G9⋮8-G9* ⋮8-G9⇔-G∈b8 9 Z.B'6Vf%&'a'R%% c#78-9:- ;0-;%⋮"∀-∈<+ H c\'-:"#78"9:%⋮" H c\'-:#789:;0;%⋮""⇒;0⋮"8K#%⋮"9 89 H c\'-:H#78H9:G0;%⋮"⇒G0⋮"8K#%⋮"9 89 g89KL89*(8;0;G09⋮"*⋮" ⇒⋮"8K# M "9 8 9 g89KL8 9*(0⋮" c3*6&'()%,0'/1%78-9:- ;0-;%⋮"∀-∈<=8=0=%∈<9= #%%>?=0=%.@%'6%" '()*+,-. 6&'()%,0'/1%78-9:- ;0-;%⋮$∀-∈<=8=0=%=$∈<KL$ M 9=#%%>?=0=%.@%'6%$ (#)%B - - 2+ + _ _ - - - - ^ ^ ^ h = + + + = + + + ÷ ÷ _ - - - - - - ! ! ^ h ! ! ! h = + + + + = + + + + ÷ ÷ ÷ - ! h = + + ÷ c# - " ! + ≥ ÷ ∀-⇒ - " ! h + + > ÷ ∀- c3*.1%- ; -;2A&%B&'>$ (#)ij%%(Rk&SV H ij-≥"#- ≥"KL -≥"⇒- ; -;2≥2`" H ijH=2l-l"#- `"∀-KL -`H!=2⇒- ; -;2`"=2`" H ij-≤H=2#-l"KL-; ≤" ⇒- ; -:-8-; 9≥"⇒- ; -;2≥2`" .B.1%- ; -;2`"∀- c3*.1%- ; -;2A&%B&'>$ (#)m "" " A = = = = ⇒ "" "" " " A = × ××× = 89 VCf&%]%,CD*E?05&=%B "" "" " " A + + + = = = = = + + + ⇒ "" "" "" " A + + + = ÷ + + + 89 g89KL89*( "" "" " " + + + = ÷ + + + (#)m "" " A = = = = ⇒ "" " A = A == A= = = ⇒ "" " A = ⇒ "" " A = mA%= "" "" "" "" " " " " " A A A A8 9 + + + + + + + + + = = ÷ ÷ + + + + + + + + + "" A= c3* "" "" " " + + + = ÷ + + + (#)c# -G*GF:"⇒-:*;F %B :-8*FG* GF 9:8*;F98*FG* GF 9 :* FG* G*F ;*F G* FGF :H* GF :HJ .BKLJML'?.?' (#)c#-G*GF:"⇒-G*:F=-GF:* ij;J :-*FG-* H-F ;* ;F :-*FG8-* G* 9G8-F GF 9 :-*FG* 8-G*9GF 8-GF9:-*FG* FGF *:*F8-G*GF9 :*F":" c3*KLJML'?.?' (#*)%BJ:* ;F :* 8-GF9;F 8-G*9:-* G* F;-F G*F :-* ;-F G8* F;*F 9:-* ;-F G*F8*;F9 :-* ;-F G-*F:H .BKLJML'?.?' ! (R\%6=%1&$'.)M n+$,-"&.,/#0 $$1,234,567 Chng minh ij∆J4%BML(&.'/$%,J=OML(&.'/$%,4%Q%1&$' OooJ4KL O J4 = (+'.?'%,'%,'OM]*.'/$P%O:OP ij∆OPKL∆O4%B O:O48&9 · · OP 4O= 8.?'.E9= O:OP8%%Cp&9 +∆OP:∆O48%&%9⇒P:4= µ µ 4= '&B% µ KL µ 4 qK)(Mr(&05&+Poo4 ij∆PKL∆J4%B :J8&9 · · P J4= 8.s&K)=Poo49 P:48%1&$'(+9 +∆P:∆J48%&%9P:J4= µ µ J= '&B% µ KL µ J qK)(.s&K)05&+OooJ4 tT'%BP:O8%%Cp&9=J4:P8%1&$'(+9+ O J4 = Tr li bi ton : g&'a'6P:PJ=P:PY⇒P:PJ:PYRu&pO:O:O4 VCf&.)Mq(+%BO: J =P: 4 ⇒P:O8: J 9=O:P8: 4 9 .BO;O;P;PY:P;O;O;P:P;O:J;4 c3*O;O;P;PY:J;4 VCf&.)Mq(+%BOooJKLPoo4 Z*( · µ JP = 8Mr(&9= · µ 4O = 8Mr(&9⇒ · · µ JP 4O = = ij0(Rk&SV ∆J4%B µ " _"< 89⇒ · · " JP 4O _"= < Y'.B H 'PJ5$&'v''PYKLP+ · · · µ " YP YPJ JP _" = + = + H 'O45$&'v''OKLO+ · · · µ " O O4 4O _" = + = + Z*( · · YP O= 8: µ " _" + 9 ij∆YPKL∆O%B PY:O8:P9 · · YP O= 8%1&$'(+9 P:O8:O9 ⇒∆YP:∆O8%&%9 ∆J4%B µ " _"> 89⇒ · · " JP 4O _"= > Y'.B H 'P5$&'v''PYKLP+ · · · · µ " " " YP YP P _" h" JP " = + = + − = − H 'O45$&'v''OKLO+ · · · · µ " " " O O O _" h" 4O " = + = + − = − Z*( · · YP O= 8: µ " " − 9 ij∆YPKL∆O%B PY:O8:P9 · · YP O= 8%1&$'(+9 P:O8:O9 ⇒∆YP:∆O8%&%9 ∆J4%B µ " _"= 8 9⇒ · · " JP 4O _"= = Z*(0.'/$Y=P=X&L&KL0.'/$=O=X&L& Y'.BA&sT'%%$&'%YPKLO+A&/ c#OooJ+ · · PO JP= 8Mr(&9 U(Rk&SV=%B∆YP:∆O⇒Y:= · · · · PY O=PY O= = L · · · · · · · · · · " Y PY PO O PY JP PY PY YP PY _"= + + = + + = + + − : " " " h" _" _"− = ∆Y%BY:= · " Y _"= +ML$&'%K&%[T' U(Rk&SV=%B∆YP:∆O⇒Y:= · · · · PY O=PY O= = L · · · · · · · · · · " Y PO PY O JP PY PY h" P PY PY= − − = − − = − − − : · · · " " " " " 8YP PY PY9 " h" _"− + + = − = ∆Y%BY:= · " Y _"= +ML$&'%K&%[T' U(Rk&SV = Y P PY 84 J9 O O 8J 49 = + = + ⇒ = + = + Y: L · · PO JP= :_" " ∆Y%BY:= · " Y _"= +ML$&'%K&%[T' B$MT'=%B∆YK&%[T' " 8- - 9 J - - - - + + + = = + + + + + %B- ;-; :- ;-;-;;:-8-;9;8-;9; :8-;9 ; c#8-;9 ≥"∀-⇒8-;9 ;≥∀- ]05&-a*(⇔-;:"⇔-:H - ;-; :8-;9 ;`"∀-+ J $- ⇔ - - + + $-⇔- ;-; $' ]*&'()w]%,- ;-; 05&⇔-:H c3*&'()M\]%,J: ; : =2⇔-:H /$01203%45 . 9 Z.B'6Vf%&'a'R%% c# 78 -9:- ;0-;%⋮"∀-∈<+ H c'-:"# 78 "9:%⋮" H c'-:# 78 9:;0;%⋮""⇒;0⋮"8K#%⋮"9 89 H. 9*(0⋮" c3*6&'()%,0'/1% 78 -9:- ;0-;%⋮"∀-∈<=8=0=%∈<9= #%%>?=0=%.@%'6%" '()*+,-. 6&'()%,0'/1% 78 -9:- ;0-;%⋮$∀-∈<=8=0=%=$∈<KL$ M 9=#%%>?=0=%.@%'6%$ . c'-:# 78 9:;0;%⋮""⇒;0⋮"8K#%⋮"9 89 H c'-:H# 78 H9:G0;%⋮"⇒G0⋮"8K#%⋮"9 89 g89KL89*(8;0;G09⋮"*⋮" ⇒⋮"8K# M "9
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Xem thêm: Hướng dẫn giải đề thi HSG Toán 7 huyện Thái Thuỵ, Tỉnh Thái Bình, năm học 2010-2011, Hướng dẫn giải đề thi HSG Toán 7 huyện Thái Thuỵ, Tỉnh Thái Bình, năm học 2010-2011