ĐỀ THI HỌC SINH GIỎI TOÁN 7 SỐ 10

     ( Thi gian 120 pht không k thi gian giao đ) !":(2 đim)  2 1 1 2 5 1 : : 2 2 3 3 2   − +  ÷    !"#$%&'(!)*+,-+./01 !"# 234!56/ !"#2 đim$4!x7 / ( ) 8 9 , :;, : < < x − + = − +  /4! x 7 , 8 , /: /< 8=.== + + = x x x !"(2 đim)/#56 :"#>?@A , : 8   < 9 B /C7DEFGF 45HFI"#JEF,9:=K/4!"#/ / LA a c c b = /LMF!DEF , , , , a c a b c b + = + #0N7(MO( JFP !"(3 đim)LA!FCLJ µ 0 A 90= ;C%L/Q(215RFSFT "AAC2 LE!UF#2N5RFSFT/VWC2 LV2(XFFJ2NT/ LMF!DEF /%LV /V%CYLV !"%(1 đim)LMF!DEF 2 2 2 2 2 2 2 2 3 5 7 19 A 1 1 .2 2 .3 3 .4 9 .10 = + + +×××+ < &'( ( Lưu : Cn b coi thi không gii thch g thêm) )*+ !" ,  -/ 012   2 1 1 2 5 1 1 9 13 8 13 16 39 23 : : : 2 2 3 3 2 2 16 6 9 6 18 18 − −   − + = − = − = =  ÷   8;=  04'(!)*+,-+.ZJ+.%/*+, ⇒ %9 0[$ !"#\A? -$%9&/ L]*8-9/#^J !"#$%9&/ =;< =/<   ( )   8 , : 8 , : 8 _ &%,Y % : : 8 +< &%+,Y % : : 8 9 , 8 9 8B , :;, : < < : < < < 8 9 89 : < < 8 , : − = − =− − − + = − + ⇔ − + = + ⇔ − + =   ⇔ − = ⇔         ⇔ x x x x x x =/,< =/,< =/,< =/,<  , , 8 , /: /< 8=.== , /9/: /:/< 8=.== := 8=.==8, K== := := , + + = ⇔ = ⇔ = = ⇔ = ⇒ = x x x x x x x x x =;,< =;,< =;,< =;,<   ];;? "#56D3"#/ @AO J% , : 8   < 9 B *8 2  , Y , Y , %,9:=K*, =;,< 4 2 -2 -4 -5 5 A 3*8 ⇒ , : 8 < 9 B a b c = = %` ⇒ , : - - < 9 B k a k b k c = = = AJ*, ⇔ , 9 K 8 *  ,9:=K ,< 8B :B k + + = ⇒ `%8.=2 `% 8.= − Y0N`%8.=;56%_,-%8:<-%:=/ VJJ%YY%,:_/ Y0N`% 8.= − ;56% _, − -% 8:< − -% := − VJJ% _, − Y* 8:< − Y* := − % ,:_ − / =;,< =;,< =;,<  3 a c c b = "($D , /c a b = VJ , , , , , , / *  / *  + + + = = = + + + a c a a b a a b a b c b a b b b a b  =/< =;<    AHK∆ 2  CKH∆ J µ µ 0 90H K= = C%L*F · · HAB KCA= *LUFa2N · KAC  ⇒ AHK = CKA∆ ∆ *F//F ($D%LV*Lbc5HFMF 8;=  3d( AHK = CKA∆ ∆ "($DC%V*Lbc5HFMF 0[$V%YV%CYLV =;< =;< % J 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 5 7 19 A 1 .2 2 .3 3 .4 9 .10 2 1 3 2 4 3 10 9 = 1 .2 2 .3 3 .4 9 .10 1 1 1 1 1 1 1 1 = 1 2 2 3 3 4 9 10 1 = 1- 1 10 = + + +×××+ = − − − − + + +×××+ − + − + − +×××+ − < =;< =;< ( Lưu : Hc sinh c cch gii khc m đ!ng th v#n cho đi$m t%i đa) A B C H K . 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 5 7 19 A 1 .2 2 .3 3 .4 9 .10 2 1 3 2 4 3 10 9 = 1 .2 2 .3 3 .4 9 .10 1 1 1 1 1 1 1 1 = 1 2 2 3 3 4 9 10 1 = 1- 1 10 = + + +×××+ = − − − − + + +×××+ −. đim)LMF!DEF 2 2 2 2 2 2 2 2 3 5 7 19 A 1 1 .2 2 .3 3 .4 9 .10 = + + +×××+ < &'( ( Lưu : Cn b coi thi không gii thch g thêm) )*+ !". !"#$%&'(!)*+,-+./01 !"# 234!56/ !"#2 đim$4!x 7  / ( ) 8 9 , :;, : < < x − + = − +  /4! x  7  , 8 , /: /< 8=.== + + = x x x !"(2 đim)/#56