 a b c d+ + + PHÒNG GD-ĐT HUYỆN LONG ĐIỀN KỲ THI CHỌN HỌC SINH GIỎI CẤP HUYỆN ------------------------------------------------ NĂM HỌC 2009-2010 ------------------------- MÔN THI : TOÁN Thời gian : 150 phút ( Không kể thời gian giao đề) Ngày thi: 16/01/2010 Ba ̀ i 1    a c b d =  !"#$%&'()*+,)%) Bài 2 -.+/"01' 2234 %'+ - - - - a b a b + ≥ −  -5'617+8 abc 9:;  ( ) - -  - abc n cba n  = −   = −   <+)!8<- Bài 3 -=>? @  A > B   C4 DDDDE -: −+−−−  @ + D ≥ -F+ B +G"? A   H:DD:-ID : - =++++ Bài 4:-JK9G"5  -  : Hx m m y m+ + − = −  3LMN',JK+O)+,'=PQ  L%'+"0R+'!+5JK)S)S+O)'T+,' N Bài 5-  ∆ U.V)+,'C0'" ∆ U.UC - 4.C - WC - 9.CX Bài 6 3  YJ"ZJR.4-[>'\N]+,'U+T"^YJ "ZF_+5+/)*+,'U8.F_+`abc5+/)*8UU. %'+U..a.WU. a4U. -  MNN"+,'U%+Ua`9+^<6X+^<6 9d[ PPPPePPPP  - - - -  L :L I: :ff P = + + + + ĐỀ CHÍNH THỨC a d b c a d b c + − − = + − − ĐA ́ P A ́ N Ba ̀ i 1('g++-+,'  - - - -  L :L I: :ff P = + + + + - - - -  :L LE Ef f- = + + + +          : L L E E f f - = − + − + − + + −   : - = − - E =  3L+,' 3L+,' 3L+,'   - - a c do ad bc ad bc b d   = ⇒ = ⇒ =  ÷   3L +,' Bài 2: -+,' hi548 ( ) ( ) ( ) - - - - - - - a b ab a b a b a b a b a b a b a b − + − + + = = = − + − − − −  h`2238G#.]Sj+- 9 ( ) ( ) - - -a b a b a b a b − + ≥ − × − − ik! - - - - a b a b + ≥ −   -+,' i+/c - - 33 3  33 3   abc a b c n cba c b a n n  = + + = −   = + + = − +   l-9ffm4mL42mL M ff:3EL CnR33 - -  fff 3 333  :n n n≤ − ≤ ⇔ ≤ ≤ ⇔ ≤ ≤ :f  L fn⇔ ≤ − ≤ 3EL - 3L+,' 3EL+,' 3L+,' 3-L+,'             a d b c a d b c a d b c + − + =     + + + + − +         a d b c = + + + -  -  a d b c a d ad b c bc + − − = + + − + + - - a d b c a d ad b c bc + − − = + + − − −  a b c d + + + l:42mL4ff424-I ik!b5' IELabc = 3L Ba ̀ i 3(  -+,' C4 DDDDE -: −+−−−  @ + D ≥ DDED −+−−= 3-L   -L   DDD −+−−−−−= 3L         −       −−−−=  -L -  DD - 3L ( )( ) -D:DD +−−−−−= 3L ( )( ) -DD:D +−−−−= 3-L -F+ B +G"? A  H:DD:-ID : - =++++  > o > @ !D4 A +8 o ') B = 3EL i @ + D3 <≤ ? A  H::-I:DD:-ID : -: - =++++<++++ p8=S+8 o ' @ + D3 <≤ 3L i @ +D2? A  H::-I:DD:-ID : -: - =++++>++++ p8=S+8 o ' @ +D2 3L i> o != @ +8 o ')!> @ D4 3-L Bài 4:-+,' i5JK+O)=PQ8  -   : H L H :m m m m m+ − + − = − ⇔ − = − ⇒ = 3L+,' F_+ ( ) 3 3 Qx y _T+,'N'+O) 9 3 3  -  : Hm x m y m m+ + − = − ∀ 3L ( ) 3 3 3 3 3 3 3 3 3 3   - : H 3   3  - : H 3 - x y m x y m x y x x y y ⇔ + − + − + = ∀ + − = = −   ⇒ ⇔   − + = =   ik!+,'N'+O)PQ- Bài 5 iq'+V)Cp  +,'  ' - - - AM BM CM= + - - - BN BM MN⇔ = + BMN⇔ ∆ )Sr+C · · · 3 3 3 f3 I3 L3BMC BMN NMC⇒ = + = + = +,' Bài 6:3 %'+U..a.WU. a4U. -  %'+%+U`a5;k3 : BCN ACM BN AM ⇒ ∆ = ∆ ⇒ = U..a.4. -  U. a4UU`4U - 42]=C+,' j U`a 4U`Ua ≤  - - - - - - - AD AE DE AH+ = = 3EL ⇒ j U`a  ≤ - - - - - - AH AO R ≤ = 3EL ik!CDj U`a 4 - - R s+U`4Ua !U+,'+;*)U.3L  O B C A H D E .     a d b c = + + + -  -  a d b c a d ad b c bc + − − = + + − + + - - a d b c a d ad b c bc + − − = + + − − −  a b c d + + + l:42mL4ff424-I. b c + − − = + − − ĐA ́ P A ́ N Ba ̀ i 1('g+ + - +, '  - - - -  L :L I: :ff P = + + + + - - - -  :L LE Ef f- = + + + + 