skkn một số phương pháp giải hệ phương trình không mẫu mực dùng bồi dưỡng học sinh giỏi lớp 9

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THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn     !" "w$% "!%\C$ 8\ $D$ U%g <m"D$!MS <$"@ <!MN "!SD "w$*;! "w$*"SD"w$*% ""w$$dLO$"w$ nb .MS <$"@ <!MN "!SD $dLO$"w$C"]!"x <*Oz!8{!|aC["w$ % "8@A$"w$;f"9C"@ <!MN "*Oz!8{n"9"L%C"@ <!MN "O$ "P!"L% Q } <;a%8`"w$% "8@A$"w$"L%kb!z$O%\ 8]%!@ <8@ <:U!"9 C"@ <!MN "n~ib!z$!"\•€~ib!z$$U <8T%?•.MS <$"@ <!MN " !SD aCW;naC["w$% "8@A$"w$m"D8{b8d;fC"@ <!MN ":U!Q "@_C"@ <!MN "O$ "P!:U!Q €C"@ <!MN "!$"€C"@ <!MN "$">LQ  :•€C"@ <!MN "$">LgP<%D!M‚!b9!8?%€C"@ <!MN "O$"L%€C"@ < !MN "$">LgP$ƒ ."x <kL;%9$"w$$D$gT <C"@ <!MN "!M= "w$% " 8@A$!ML <O‚!@ <8?%8{b8d;f$D$C"@ <C"DC<%l%$D$C"@ <!MN "8T% ?*8%f nb8„ < <"…L;a%;%9$"w$% "8@A$!ML <O‚$D$C"@ <C"DC<%l% "9C"@ <!MN "m"x <C"l%n"9"L%C"@ <!MN "O$ "P!"L%Q  D$"9C"@ <!MN ":n$D$"<%l%!†!"U$;nS8c$8%e:M%= <$dL"9* m"x <$`:U!8@‡ <?%$" <$"S;%9$<%l%$D$"98`*!L<w%$D$"9gT < nb n,%9$<%l%$D$"9C"@ <!MN "m"x <:• :#$8ˆ%"‰%"w$% "C"l% z:MP!;Š <$D$C"@ <C"DCO%\ 8]%!@ < 8@ <:U!"9C"@ <!MN "*$D$C"‹CO%\ 8]%!@ <8@ <:U!C"@ < !MN "*8c$O%9!"w$% "C"l%MP!!% "ŒC"D!"%9 ML "Š <8c$8%e:MP!M%= < $dL!| <"9!|8`$`$D$"O%\ 8]%"AC "‡8`:a%$`!"e<%l%8@A$"9 JP% V#23A& .b!MS < U%g <$"@ <!MN "!SD aCW;naC[8•!ML <O‚$"S"w$ % "m"D8{b8dm%\ !">$;fC"@ <!MN ";n"9C"@ <!MN "8T%?$} <$D$ C"@ <C"DC<%l%.MS <m"%8`*;%9$!ML <O‚$D$C"@ <C"DC<%l%"9C"@ < !MN "m"x <:•:#$"{ "@m"x <8@A$8f$C!a%!MS <D$"<%DSm"SL;n <Lb$l"9!"? <D$"!"L:m"lS"%9 $`gn "$"S"w$% "!M <"w$$ ,%9$<%l%8@A$$D$"9C"@ <!MN "m"x <:•:#$8ˆ%"‰%"w$% " C"l%; g7 <MP!m"‹S‹S$D$m%\ !">$8•"w$8e$`8@A$$D$"O%\ 8]%"AC 8?%;a%M%= <!| <"9C"@ <!MN "8•$"S*8%f nb8D "<%D8@A$!MN "8U m%\ !">$$dL"w$% "" ";N;b*!MS < U%g <$D$8f!"%"w$% "<%‰% Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn '    !" $PC!Ž ":x !SD [*8f!"%!be % ";nS!M@‡ <.4.$"b= @ <h= * 8f!"%m"lSD!$"P!@A <"w$mN:x !SD [ "%f ƒ:<{ 8•b$dL %DSg7$;nnS!TS@ <h= x RP!"%9 $D$$•"‰%b=${"w$% " C"l%<%l%$D$"9C"@ <!MN "m"x <:•:#$*;a%:7$8$"C"• ST%8?% !@A <"w$% ""x < "Š <;b*!MS < U%g <8f!"%!be % ";nSm"?% .4.$"b= $dL!M@‡ <T%"w$i?$<%L*T%"w$@C"T:nU%:x !SD ;ˆ <*;ˆ <x RP!"%9 $D$$•"‰%<%l%"9C"@ <!MN "!"U$ m%e"9m"x <:•:#$ .n%%9!"L:m"lS8?%;a%$D$<%DS;%= C"7!MD$"O„%g@• <"w$% " <%‰%;%\!M%= <$"S$"b= 8f<%l%"9C"@ <!MN "m"x <:•:#$m"x <$`* $" ";N!"\<%DS;%= gTb<cCMP! "%fm"`m"ƒ ;ny <!y <m"%gTb8\ $"b= 8f nb,N;b*m"%gTb8\  U%g < nb<%DS;%= !"@‡ <gTb@a! kLO‘ <:U!?;g7:% ""ST$"@Ln:M’8@A$ "Š <8@‡ <?%$" <8e <%l%$D$"9C"@ <!MN "m"x <:•:#$ " ";N "Š <gS:L <! " ;n!"#$!\!M= :n!x%$"w D < m%\ $dL:N "n~  !"#$% PYZBZ[\]^SB\_ ^SP LP`3aW3#Z&#*/>`&'#?&3b1 D <m%\ m% " <"%9: nb "‘::7$8$"!C"AC*zCR\C"9!"? < $D$C"@ <C"DC!"@‡ <8@A$“g7 <8e<%l%"9C"@ <!MN "m"x <:• :#$g} <O„%g@• <"w$% "<%‰%aC[$dL$PC!M <"w$$ "%9:;7${ 8T!_ ”"ŽML8@A$m%\ !">$;f"9C"@ <!MN "$`%= kL :n"w$% "${ z:;Š <!M@a$m"%!%\C$ ;a%$D$C"@ <C"DC<%l%"9C"@ <!MN "m"x < :•:#$ ”@LML"9!"? <$D$C"@ <C"DC<%l%"9C"@ <!MN "m"x <:•:#$ $`#zCR\C"ACx<$;f:c!!@gbm%\ !">$OU:x  Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn 6    !" ”••bg# <8@A$"9!"? <$D$On%!CC"}"AC;a%8?%!@A <"w$% " !"–S!| <C"@ <C"DC$7!"e* "‘:<%yC"w$% "$`8@A$On%!Cb9 !C m"z$•m%\ !">$*<%DS;%= <%l <gTb$`8@A$"9!"? <On%!C:% ""ST C"S <C"y$"S!> <C"@ <C"DC JP!$c&'&'#?&3b1 ?%!@A < <"%= $>$dLD <m%\ m% " <"%9: nbn"9!"? <$D$ C"@ <C"DC<%l%"9C"@ <!MN "m"x <:•:#$* "Š <8%e:"w$% "${ @Œm"%!%\ "n "<%l%$D$"9C"@ <!MN "ST% nb MP#$%&'"#("&'#?&3b1 e"Sn !"%9 D <m%\  nb!x%8•“g7 <$D$C"@ <C"DC <"%= $@L_ ”4"@ <C"DCgb;!O%9 $"> <;ngb;!‚$"“ ”4"@ <C"DC!M|!@A <"SDm"SL"w$ ”4"@ <C"DCC"• !$"!] <"AC ”4"@ <C"DCSD "*8?%$"%\*!"? <m= ”4"@ <C"DC?%9*"9!"? <"SD—C"‰ <;P *8%f!ML*m"lSD! 8%f!ML!"#$!\ dPeS Pe[\_fg_dhi\_h Rj LP*#k"#$%&'+,&#6X3&#l#km& E&#&'#nk 9"L%C"@ <!MN "O$ "P!"L%Q n"9$`gT <_ ˜™ š š š˜™         + =   + =  !MS <8`L*O*$*L›*O›*$›n$D$?$"S!M@a$*   v + ≠ ;n   š š v + ≠  <"%9:$dL"9n$cC? ( ) €  !"Sl:• 8„ <!"‡%"L%C"@ <!MN "˜™ ;n˜™$dL"9%l%"9!>$n!N:!P!$l$D$ <"%9:$dL"9 (3#') Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn B    !" .MS <$"@ <!MN "!SD !M <"w$$8e<%l%"9"L%C"@ <!MN "O$ "P!"L%Q !L!"@‡ <“g7 <"L%C"@ <C"DC_ ”4"@ <C"DC!"\ "‡“g7 <kb!z$!"\€ ”4"@ <C"DC$U <8T%? "‡“g7 <kb!z$$U <8T%? e:% ""ST$"S"L%C"@ <C"DC nb!LR‹!;g7L_ BW4`P%l%"9C"@ <!MN " '  6˜™  B˜™     − =   + =  &'( D$"_ ”.|C"@ <!MN "˜™$dL"9*My!!"–S!L$` B  = − ."Lb;nSC"@ < !MN "˜™$dL"9!L8@A$_ ( ) '  B  6 − − = Lb V 6 =  ”."–Skb!z$!"\"9C"@ <!MN "8•$"S!@ <8@ <;a%"9C"@ <!MN " L_ V 6  B        = =   ⇔   = − =   ,b"9$` <"%9:gb "P! ( ) ( ) € €   = D$"_ !"#$ ”"• $l"L%;\$dLC"@ <!MN "˜™;a%M„%$U <;a%C"@ <!MN "˜™;\ ;a%;\!L8@A$_ ( ) ( ) 6  '  v 6   + + − = + Lb V 6 =  ”."–Skb!z$$U <8T%?"9C"@ <!MN "8•$"S!@ <8@ <;a%"9 C"@ <!MN "L_ V 6   B       = =   ⇔   + = =   ,b"9$` <"%9:gb "P! ( ) ( ) € €   = )*+,(.MS <$"@ <!MN "!SD aCv$dL$PC.4."w$% ":a%Oz! 8{!%\C$ 8\ ;%9$<%l%"9C"@ <!MN "!M= O‘ <C"@ <C"DC“g7 < 8‚ "!">$$PCE‘ <C"@ <C"DC“g7 <8‚ "!">$!L$`!"e<%l%"9 C"@ <!MN "!M=  "@L_ 9C"@ <!MN " '  6  B     − =   + =  $`_ Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn o    !" '  6  '6 '  V v€ 6 B 6€ 'B 6 V  B B   % % % − − = = + = ≠ = = + = = = − = bML"9$` <"%9:gb "P!_ 6  V V  V   %  % %  %  = = =     = = =   JP*"#$%&'+,&#a!ob&';Fp/ E&#&'#nkU!"9C"@ <!MN ""L%Q R*b8@A$<w%n"9C"@ <!MN "8?% R> <ST%:U! \:œ%C"@ <!MN "$dL"98•$"S8?%R> <;a%"L%Q R;nb ˜ <"…Ln:œ%C"@ <!MN "$dL"9m"x <!"Lb8]%m"%!L8]%;L%!Mˆ$dLR;nb $"S "L™ W&#3#l\˜R v €b v ™n:U! <"%9:$dL"9!"N˜b v €R v ™$• <n <"%9:$dL "9 (3#')#$q&'45&'c!   = + ;n 4 = *;a%8%fm%9    64 v− ≥ 8@L "98•$"S;f"98 <%l " 8•O%\!$D$"<%l% BW4`P%l%"9C"@ <!MN " ( )    ' W        + + =    + + + =   &'( c!   = + ;n 4 = *m"%8`"98•$"S$`gT <_  ˜™  ' W˜™  &  &  + =   − + =  .|˜™bML &  = − *!"Lb;nSC"@ <!MN "˜™!L8@A$_ ( )     ' W"Lb B Bv v    − − + = + − = 4"@ <!MN " nb$`"L% <"%9:C"• O%9!_ B€ v = = − ž\ B = !"N o*& =  = 'n$D$ <"%9:$dLC"@ <!MN "O$"L%_ ( ) ( )   B o v  ' v '       =  − + = ⇔ − − = ⇔  =  bML ( ) ( ) € €'  = "Sc$ ( ) ( ) € '€   = ž\ v = − !"N *& =  = 'n$D$ <"%9:$dLC"@ <!MN "O$"L%_ Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn V    !" ( ) ( ) ' v  v ' V v V       = −  + + = ⇔ + + = ⇔  = −  bML ( ) ( ) € '€ V  = − − "Sc$ ( ) ( ) € V€ '   = − − ,b"9C"@ <!MN "8•$"S$`6 <"%9:_ ( ) ( ) ( ) ( ) €' € '€  € '€ V € V€ ' − − − −  MP*"#$%&'+,&#a!ob&';Fp#k E&#&'#nkU!"9C"@ <!MN ""L%Q R*b8@A$<w%n"9C"@ <!MN "8?% R> <ST%"L% \!MS <"9C"@ <!MN "*m"%8]%;L%!Mˆ$dLR;nb$"S "L !"NC"@ <!MN " nb!M!"n "C"@ <!MN "m%L W&#3#l\˜R v €b v ™n:U! <"%9:$dL"9!"N˜b v €R v ™$• <n <"%9:$dL "9 (3#')#$q&'45&'.M|$D$;\!@ <> <$dL"L%C"@ <!MN "!"N "  8@A$C"@ <!MN "!$"gT < ( ) ( ) ( ) v Ÿ * v Ÿ * v         − =  − = ⇔  =  .|8`"98•$"S!@ <8@ <;a%"L%"98 <%l " $`!"e<%l%8@A$ BW4`P%l%"9C"@ <!MN "L_ ' '   ˜™   ˜™      + =   + =   &'( .M|!| <;\$dLC"@ <!MN "˜™$"SC"@ <!MN "˜™!L8@A$_ ( ) ( ) ( ) ' '          v ' v˜   v * ™  6                       − = − ⇔ − + + + =   ⇔ − = + + + = + + + > ∀  ÷   ⇔ = V × ."Lb  = ;nSC"@ <!MN "˜™!L8@A$_ ( ) ( ) '     v   v  B         =   − + = ⇔ − + − = ⇔ − ±  =   Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn W    !" ,b"9C"@ <!MN "8•$"S$`' <"%9:n_ ( )  B  B  B  B € € €  € €          − − − − − + − +  ÷  ÷  ÷  ÷     Pe[\_h\_fgrsSt LP#$%&'"#("6D&au$%&'a$%&' eO%\ 8]%!@ <8@ <:U!"9C"@ <!MN "$"y <!L“g7 <$D$kb !z$O%\ 8]%!@ <8@ < "@kb!z$!"\*kb!z$$U <8T%?} <;a%8`!L ${ m\!"AC$D$C"‹CO%\ 8]%!@ <8@ <:U!C"@ <!MN "!MS <kD!MN " O%\ 8]% "@kb!z$$"be ;\*kb!z$ "• *C"• !$"!"n "!$"*ON " C"@ <"Sc$CC"@ <"L%;\*!"=:Oa!n:RP!"%9  "• !“$" <*— "N $" <;%9$O%\ 8]%!@ <8@ <$D$"9C"@ <!MN "ST% nb8ˆ% "‰% <@‡%n:C"l%MP!m"‹S‹S;n% ""ST!!MS <!| <O@a$O%\ 8]%.L$` !"e; g7 <C"@ <C"DCO%\ 8]%!@ <8@ <8e<%l%"9m"x <:•:#$ !MS <$D$!N ""? <L L+F&'#*3v/"#$%&'+,&#6X3&#la!><m&o#k@m&@P BW4`L%l%$D$"9C"@ <!MN "L_     v  v      − + =   − + − =  &'( .L$`_  ( ) ( ) ( )       v   v        v   B  v    v v                               − + =   − + − =  = −   ⇔  − − + − − =   = −   ⇔  − =    = −  = −       = =     ⇔ ⇔   = − =       = =       ,b"9$`"L% <"%9:_ ( ) ( ) €v € € − Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn [    !" #X&ow&()*+,-)"./ 0123445346"7,48+!"*' 349:- ;<" =>4<"- ;0+,.'? 0 @"A" ;= >4+?""A"/' @B34C()6"7,4 ("=>D01B346"7,4 ("*'"/7"" E""34#FG/(!7) "#$= BW4`J%l%$D$"9C"@ <!MN "L_ ( ) ( )      ' 6 ˜™  ˜™  + + + = − +   + + =            &'( " !"Pb v = m"x <!"Sl:• C"@ <!MN "˜™$dL"9 = "9m"x <$` <"%9: ( ) v€  "% v ≠ !|C"@ <!MN "˜™!L$`       − + = !"Lb;nSC"@ <!MN "˜™!L 8@A$_ ( ) ( ) ( ) ( ) ( ) ( )              ' 6         '          v       B                                       − − + = − +   ÷ ÷      −  + =    − − = − −  ⇔  − + =    =   =     = − − + =     = −     ⇔ ⇔ ⇔   = −  −   + = −   + =     = −       ,b"9C"@ <!MN "8•$"S$` <"%9:n_ ( ) B €  € €     − − −  ÷   Gi¸o viªn: NguyÔn V¨n HiÕn - THCS §oµn ThÞ §iÓm, Yªn Mü, Hng Yªn v [...]... y = 1 9 y = 1 x = 3y x = 3y x = 3y 2 x 2 + y 2 = 1 2 ( 3 y ) 2 + y 2 = 1 19 y 2 = 1 3 19 3 19 2 2 x = x = x = 3 x = 3 19 19 hoặc hoặc hoặc y = 1 y = 1 y = 19 y = 19 3 3 19 19 Giáo viên: Nguyễn Văn Hiến - THCS Đoàn Thị Điểm, Yên Mỹ, Hng Yên 14 Mễễ T Sễ PHNG PHAP GIAI Hấễ PHNG TRINH KHễNG MU MC DUNG BễI DNG HOC SINH GIOI LP 9 Võy hờ a cho cú 4 nghiờm: 19 2... 4 nghiờm: 19 2 1 2 1 3 19 ; ữ; ; ữ; ; ữ; 19 3 19 ữ 3 3 3 3 19 19 ; ữ 19 19 ữ Nhõn xet: Trong hờ phng trinh trờn, phng trinh th nhõt chinh la phng trinh ng cõp bõc hai, tuy nhiờn ụi vi hoc sinh lp 9 khụng nờn giai bng cach t x = ky vi vi cach giai nay hoc sinh rõt kho hiờu tai sao lai nghi ra cach t o Chinh vi võy, khi day giao viờn nờn hng dõn hoc sinh hay phõn tich phng trinh... hoc sinh lp 9 Vi du 5: Giai hờ phng trinh sau x3 y 3 = 9 (Thi học k ì 2 lớp 9 năm học 2011- 2012 Sở H ng Yê n) 2 2 x + 2 y = x 4 y Li giai: x3 y 3 = 9 2 2 x + 2 y = x 4 y 3 3 x y = 9 2 2 3 ( x + 2 y ) = 3 ( x 4 y ) x3 y 3 = 9 x3 y 3 = 3 x 2 3 x + 6 y 2 + 12 y + 9 2 2 2 2 3 x 3 x + 6 y + 12 y + 9 = 9 x + 2 y = x 4 y ( x 1) 3 = ( y + 2 ) 3 x 1 = y + 2 2 2 2 2 x + 2 y... 1) y 3 ( 2 y 1 ) y = 4 y ( 2 y 1 ) x = 2y 1 x = 2y 1 3 2 2 10 y 19 y + 10 y 1 = 0 ( y 1) 10 y 9 y + 1 = 0 ( ) x = 2y 1 41 1 41 1 y = 1 x = x = x = 1 10 10 hoặc hoặc 9 + 41 y= y =1 y = 9 + 41 y = 9 41 20 20 20 9 41 y = 20 Võy hờ a cho cú 4 nghiờm la: 41 1 9 + 41 41 1 9 41 ; ; ữ; ữ 10 20 ữ 10 20 ữ ( 0; 0 ) ; ( 1; 1) ; Nhõn xet: ờ giai... SINH GIOI LP 9 xy ( x 2 y + 1) = 0 x + y + xy ( 3 x y ) = 4 xy x = 0 x + y + xy ( 3 x y ) = 4 xy y = 0 x + y + xy ( 3 x y ) = 4 xy x = 2 y 1 x + y + xy ( 3 x y ) = 4 xy ờn õy viờc giai hờ ban õu c a vờ viờc giai 3 hờ phng trinh n gian hn Cach biờn ụi nay kha n gian nờn hoc sinh kha dờ tiờp thu, c biờt la hoc sinh lp 9 Vi du 5: Giai hờ phng trinh sau x3 y 3 = 9 (Thi học. .. giai c hờ phng trinh trờn nh trờn la kha kho ụi vi hoc sinh, c biờt la hoc sinh lp 9 Vi vi du nay, oi hoi hoc sinh phai nhõn xet hờt sc tinh tờ Giáo viên: Nguyễn Văn Hiến - THCS Đoàn Thị Điểm, Yên Mỹ, Hng Yên 13 Mễễ T Sễ PHNG PHAP GIAI Hấễ PHNG TRINH KHễNG MU MC DUNG BễI DNG HOC SINH GIOI LP 9 cac hờ sụ cua tng hang t trong mụi phng trinh va hoc sinh a c tiờp cõn vi cach biờn ụi tng t nh trờn BI TP... = 9 2 2 hoặc 2 v = 2 ( 4 v ) + 7 v = 3 v = 5 v = 2.u + 7 v + 2v 15 = 0 u = 1 thay vao cach t õn phu ta c: v = 3 * Vi x2 + 1 = 1 y = x2 + 1 x2 + x 2 = 0 x = 1 x = 2 hoặc y y = 2 y = 5 y = 3 x y = 3 x x + y = 3 u = 9 thay vao cach t õn phu ta c: v = 5 * Vi x2 + 1 =9 9 y = x 2 + 1 x 2 + 9 x + 46 = 0 y y = 5 x y = 5 x x + y = 5 Hờ nay vụ nghiờm vi phng trinh x 2 + 9 x... 2 z 2 y + z + x =9 ) x 2 = ( y 1) ( z + 2 ) 8) y 2 = ( z 1) ( x + 2 ) 2 z = ( x 1) ( y + 2 ) C THC NGHIM S PHM I GIO N DY THC NGHIM Di õy tụi xin gii thiờu mụt giao an ca mụt tiờt trin khai sang kiờn sau khi hoc sinh lp 9 a c hoc xong cụng thc nghiờm ca phng trinh bõc hai tai lp 9B trng THCS oan Thi im nm hoc 2012 - 2013 A - MC TIấU: Sau khi hoc xong tiờt hoc nay: - Hoc sinh nm c mụt sụ... 4 13 Khi đó ta đ ợc nghiệm của hệ l( x; y ) ( 1; 1) ; ; ữ 5 5 x= *) Khi x = y + 2 y = 2 x thay vao (2) ta cú : 2 ( x 2 2 x + 1) = 0 x = 1 Khi đó ta đ ợc nghiệm của hệ l( x; y ) = ( 1; 1) 4 13 Vậy tập nghiệm của hệ đã cho l ( x; y ) ( 1; 1) ; ; ữ 5 5 - Viờc phõn tich a thc vờ trai cua phng trinh th nhõt cua hờ, giao viờn khi day nờn hng dõn hoc sinh s dung hng ng thc ang nh ờ... (1) (Thi HSG tỉnh H ng Yên năm học 2010-2011) 2 2 y ( x + y ) = 2 x + 7 y + 2 (2) Li giai: * Nhõn thõy moi cp sụ ( x; y ) vi y = 0 u khụng phai la nghiờm ca hờ * Khi y 0 , chia ca hai vờ ca (1) va (2) cho y ta c hờ: Giáo viên: Nguyễn Văn Hiến - THCS Đoàn Thị Điểm, Yên Mỹ, Hng Yên 19 Mễễ T Sễ PHNG PHAP GIAI Hấễ PHNG TRINH KHễNG MU MC DUNG BễI DNG HOC SINH GIOI LP 9 x2 + 1 y + ( x + y) = 4 2 . 9 1 33 3 2 1 19 1 2 3 1 2 2 3 3 hoặc 1 1 3 x xy y x y x y x y x y x y x y x y y y x y y x yx y x y x y y y y x x y y = = = = 3 19 3 19 19 19 hoặc hoặc 19 19 3 19 19 x. !" ,b" ;9 8•$"S$`6 <" %9: _     − − − −      ÷  ÷  ÷  ÷  ÷  ÷         2 1 2 1 3 19 19 3 19 19 ; ; ; ; ; ; ; . 3 3 3 3 19 19 19 19 #X&ow. 1 2 1 2 1 1 10 9 1 0 10 19 10 1 0 2 1 41 1 41 1 1 1 10 10 hoặc hoặc 9 41 1 9 41 20 20 9 41 20 x y y y y y y y y y x y x y y y y y y y x y y x x x y y y y y 9 41 20 ,b" ;98 $"S$`6