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a)Haimtphng()v()ct nhautheomtngthngkhi vchkhihaivectphỏp tuynkhụngcựngphng. Vtrớtngicahaimtphng ! "#$%$&$'() !*" ! +"+#$+%$+&$'+() !*+" ( ) CBAn ;; = ( ) ';';'' CBAn = %! " ,! +" +++ -"! ",./012! +" "! "3434! +" ''' D D C C B B A A === ''' D D C C B B A A == Chựmmtphng Haimtphng()v()ct nhautheomtngthngd 5617689,6:;<472=/chuứm maởt phaỳng/ !#$%$&$'"$à!+#$+%$+&$'+"()> ? $à ? )!?" @1,.A!?"=/6@1,.A/889,6: B' 4-89,6:!α * ">!α ? ">!α C "=D=@17,46@1,.A !α * "?#E%$&$*()>!α ? "#$C%E&$?()>!α C "E?#$?%$C&$C() *"@82!α * "F,!α ? " ?"2GH,6@1,.A89,6:!α";24,%GH !α * "F,!α ? "0/I2;I2GJ8K ) (!*L?L*" 22 ( ) 1;1;2 1 −= n ( ) 1;3;1 2 −= n %!αậ * " ,!αắ ? "⇔?E** *CE*≠ >=/0G,166,%GH M 6@1,.A89,6:!α"4<7 λ!?#E%$&$*"$µ!#$C%E&$?"()>λ ? $µ ? ≠) % !?λ$µ"#$!Eλ$Cµ"%$!λEµ"&$λ$?µ() K ) (!*L?L*"∈!α"GN !?λ$µ"*$!Eλ$Cµ"?$!λEµ"*$λ$?µ()⇔?λ$Oµ() λ$Pµ()⇔ 4λ(P,Aµ(E* 6@1,.A89,6:!α"=/ Q#EQ%$R&$?() C"2GH,6@1,.A89,6:!β";24,%GH!α * " 0/!α ? "0/3434012,.7% P"2GH,6@1,.A89,6:!γ";24,%GH!α * " 0/!α ? "0/04N489,6:!α C " M 6@1,.A89,6:!β"4<7 !?λ$µ"#$!Eλ$Cµ"%$!λEµ"&$λ$?µ() S!β"TT%GNG534H%,.46@1,.A!β"-U) !Eλ$Cµ"() 4λ(C,Aµ(* 6@1,.A!β" Q#$?&$R() M @1,.A89,6:!γ"4<7 !?λ$µ"#$!Eλ$Cµ"%$!λEµ"&$λ$?µ() 89,6:!γ"40G,166,%GH ( ) µλµλµλ −+−+= ;3;2n ( ) 3;2;2' −= n 89,6:!α C "40G,166,%GH 289,6:04N4GN 0' = nn !?λ$µ"!E?"$!Eλ$Cµ"V?$!λEµ"VC() ECλ$µ() 4λ(*,Aµ(C 6@1,.A!γ" R#$O%E?&$Q() ⇔ ⇔ ⇔ /2* WG,0X,.S,@1I4H289,6:46@4,.A "#$?%E&$R()0/?#$C%EQ&EP() 22 289,6:F,0A*?E*≠?CEQ -"#E?%$&$C()0/?#E%$P&E?() 22 289,6:F,0A*E?*≠?E*P 22 289,6:F,0A***≠??E? 22 289,6:34340A 22 289,6:,./0A "#$%$&E*()0/?#$?%E?&$C() <"C#E?%EC&$R()0/Y#EZ%EY&ER() G"#E%$?&EP()0/*)#E*)%$?)&EP)() 3 2 3 5 9 6 9 5 − − = = ≠ − − − 40 4 20 2 10 1 10 1 − − == − − = /2?WIX2,.X=0/8IGJ9689,6:3<N% 3434012 "?#$=%$?&$C()0/8#$?%EP&$Q() -"?#$%$8&E?()0/#$=%$?&$O() 22 "[GJ289,6:3434,AI2GD\2G5D0/I=/ 2 2 3 2 -4 7 l m = = = ⇔ 2 2 = 4 -4 = 1 2 2 -4 m l µ λ = ⇔ = 4 1 2 m l = ⇔ = 2 1 -2 1 2 8 m l = = = 2 1 1 2 1 2 l m = ⇔ = /2C4289,6:46@1,.A ?#E8%$C&EZ$8()0/!8$C"#E?%$!R8$*"&E*)() 122,.X/48IGJ289,6:I4 "]434012^ -"./^ "F,^ 22 "]434012^ 2 3 -6 (*) 3 2 5 1 10 m m m m + = = = + + − 2 3 2 m m = + 2 3 3 5 1m m = + + 1m⇔ = 8(*,A\4N,4!_" 5%\4N42,.X/48IGJ289,6:TT -"./\28(* "F,\28≠* ⇔ /2P2GH,6@1,.A89,6:,.484`2,.@1/1763 "2GH,6@1,.A89,6:!α";I2GJ8K ) (!?L*LE*" 0/I2;24,%GH!α * "F,!α ? " -"2GH,6@1,.A89,6:!β";24,%GH8a %$?&EP()0/#$%E&EC()I4D,1/2/34340128a#$%$&E?() !α * "#E%$&EP() !α ? "C#E%$&E*() M 6@1,.A89,6:!α"4<7 λ!#E%$&EP"$µ!C#E%$&E*"()>λ ? $µ ? ≠) % !λ$Cµ"#E!λ$µ"%$!λ$µ"&EPλEµ() K ) (!?L*LE*"∈!α"GN EPλ$Cµ()!λ$Cµ"?E!λ$µ"V*$!λ$µ"!E*"EPλEµ()⇔ 4λ(C,Aµ(P 6@1,.A89,6:!α"=/ *R#EQ%$Q&E*Z() M 6@1,.A89,6:!β"4<7 λ!%$?&EP"$µ!#$%E&EC"()>λ ? $µ ? ≠) % µ#$!λ$µ"%$!?λEµ"&EPλECµ() 289,6:3434 ⇔ ⇔ 2 - -4 - 3 1 1 1 -2 µ λ µ λ µ λ µ + = = = λ(µ() b4N4!β" "2GH,6@1,.A89,6:!γ";24,%GHC#E%$&E?() 0/#$P%ER()/I4D,1/204N489,6:?#E&$Q() M @1,.A89,6:!γ"4<7 !Cλ$µ"#$!Eλ$Pµ"%$λ&E?λERµ() 89,6:!γ"40G,166,%GH ( ) λμλ-μλn ;; 4++3= ( ) 102= -n ;;' 89,6:?#E&EQ()40G,166,%GH 289,6:04N4GN 0' = nn !Cλ$µ"!?"$!Eλ$Pµ"V)$!λ"!E*"() Rλ$?µ() 4λ(E?,Aµ(R 6@1,.A!γ" #E??%$?&$?*() ⇔ ⇔⇔ RWIX2,.X=>8IGJ-89,6:3IN%/I2 ;845,I@1/,: R#$=%$P&$8() C#EQ%$&EC() #EY%E?&$R() 22 *289,6: C#EQ%$&EC() #EY%E?&$R() 0/ F,,G4I@1,:< 47,.GN<?<2GJ86N-2G5, K0/,%,47I45K0/0/46@1,.AR#$=%$P&$8() ,A8I@17=(ERL8(E** ? K9,6:,@-I2;24,%GH289,6:\2GN 6@1,.A44<76@1,.A/8 !C#EQ%$&EC"$à!#EY%E?&$R"()> ? $à ? ) !C$à"#E!Q$Yà"%$!E?à"&EC$Rà() 489,6:,@- R#$=%$P&$8() 5%C$à(R!*"LQ$Yà(El (2) LE?à(P!C"LEC$Rà(8!P" ,@/!*"L (3) ta coự: (?à(E1 %(?à(E1 vaứo (2) va(4) ủửụùc:l= -5 vaứ m=-11 . /2 ?WIX 2 ,.X=0/8IGJ9689,6:3<N% 343401 2 "?#$=%$?&$C()0/8#$?%EP&$Q() -"?#$%$8&E?()0/#$=%$?&$O() 2 2 "[GJ 2 89,6:3434,AI2GD2G5D0/I=/ 2 2 3 2 -4 7 l m = = = ⇔ 2 2 = 4 -4 = 1 2 2 -4 m l µ λ = ⇔ = 4 1 2 m l = ⇔ = 2 1 -2 1 2 8 m l = = = 2. 2 89,6:F,0A*?E*≠?CEQ -"#E?%$&$C()0/?#E%$P&E?() 2 2 2 89,6:F,0A*E?*≠?E*P 2 2 2 89,6:F,0A***≠??E? 2 2 2 89,6:34340A 2 2 2 89,6:,./0A "#$%$&E*()0/?#$?%E?&$C() <"C#E?%EC&$R()0/Y#EZ%EY&ER() G"#E%$?&EP()0/*)#E*)%$?)&EP)() 3. /2 ?WIX 2 ,.X=0/8IGJ9689,6:3<N% 343401 2 "?#$=%$?&$C()0/8#$?%EP&$Q() -"?#$%$8&E?()0/#$=%$?&$O() 2 2 "[GJ 2 89,6:3434,AI2GD2G5D0/I=/ 2
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Xem thêm: vi tri tuong doi 2 mp 12, vi tri tuong doi 2 mp 12
