    2 3 3 2 2 : 1 (víi 0, 9) 9 3 3 3 x x x x x x x x x x     + − + − − ≥ ≠  ÷  ÷  ÷  ÷ − + − −         ! x "   − ! #$  =y x %&' %  y m x m = + − + %(  )*"+,#$%&  -%(././0%&1"234 " 5642789!:      ;       y x y y x y  − =  +    + =  +  # 2789!:    x mx + + = %<! m "=         %  % x x x x − + − "1 9,->?!9,->"@%   ? x x .4234A% " B"7C9D3E"7CFGHI9JB"7C9D.>"%H-8 H?K(LM2M'N"7C9D3E0H1O<PQR'/@'N H%R ∈ H?FQHP'/@'NO%P ∈ OIR0HP1S<  :H.23A@OS  :HPTHOUS  :HR<OR<HO $ 9V:   < < a b b a     + + + >  ÷  ÷     ?'N ?   a b > WWWWWWWWWWWWRXWWWWWWWWWWWW R JG#:YYYYYYYYYYYYYYY<Z$(:YYYYYY  %&'() 3:)N ? [x x ≥ ≠ @:         + − − + + − − − − + + − − =  ÷  ÷      ÷  ÷ − + − − + − −         2 3 3 2 2 2 ( 3) ( 3) 3 3 2 2 3 A= : 1 : 9 3 3 3 ( 3)( 3) 3 x x x x x x x x x x x x x x x x x x  \        %   : % %   % %   % %   x x x x x x x x x x x x x x x x x x − + + − − + − − − − + − = = × = = + − − + − + + + + ! x "   −    −     [ \ \   x x x x − − ⇔ = ⇔ + = ⇔ = ⇔ = + %-] ?  [x x ≥ ≠ < )^   − F \x = < !*+ ,-./0 *  =y x @69,: x W W W     y [      [ &789!"_"A%&'%(:    %   %   %x m x m x m x m= + − + ⇔ − + + − = I % m − + I m − @: [ ]   %  <<%  \ [  m m m m m ∆ = − + − − = + + − +  + + > ∀ 2 ( 1) 20 0 víi m m  ⇒ &789!%@4234 ⇒ %(././0%&1"234 3:  − =  +    + =  +  2 2 2 2 10 5 1 1 (I) 20 3 11 1 y x y y x y `a = 2 x u % ≥ 0u ' = + 2 10 1 y v y R4%b9c: − = − = = =     ⇔ ⇔ ⇔     + = + = − = =     5 1 10 2 2 13 13 1 3 2 11 3 2 11 5 1 4 u v u v u u u v u v u v v  )N = = = 2 1 1 1u x x )N = = = + = + = 2 2 2 10 4 4 4 10 4 0 1 1 2 y y v y y y y B.1>4%b"'N = = = 1 1; 2 hoặc 2 x y y <)^4%b@4%II%I 1 2 I%WII%WI 1 2 #*/1234.563/* + + = 2 2 1 0 (1)x mx +78* = ' 2 1m `2789!@4234 1 2 , x x ! < > > > 2 1 ' 0 1 0 1 m m m d)d@: + = = 1 2 1 2 2 (I) 1 x x m x x d"e@:= + = + 2 2 2 2 4 2 4 2 1 1 2 2 1 1 2 2 ( 2012) ( 2012) 2012 2012x x x x x x x x = + + = + + 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 ( ) 2 2012( ) ( ) 2 2( ) 2012 ( ) 2x x x x x x x x x x x x x x x x 4%b'=@: = 2 2 2 (4 2) 2012(4 2) 2m m + 2 2 2 2 2 (4 2) 2.(4 2).1006 1006 1006 2m m + + 2 2 2 2 (4 2) 1006 (1006 2) -(1006 2)m ="19,->F = = = 2 2 2 4 2 1006 0 4 1008 252m m m = = 6 7 6 7 m m -"eF42789!@4 P"@=W%\ T * + Chng minh CB l phõn gic ca gc DCE @: ã ã ằ DCB CAB (cùng chắn BC)= ã ã BCE CAB (góc có cạnh t ơng ứng vuông góc)= O"@H.23A@OS b) Chng minh BK + BD < EC =fgOS@: EK CD (BK CD) B là trực tâm của CDE DH CE (CH AB) CB DE tại F H."7CAgOS<hH.23A@OSJgOS 31 ã ã CED CDE = haF: ả à 1 1 D E (góc có cạnh t ơng ứng vuông góc)= O"@gHOS31H BD = BE HOTHPHSTHPSP 9PS'/1P@:SPUS%1e.N> HPTHOUS c) Chng minh BH . AD = AH . BD =fH@: ã 0 ACB 90 (góc nội tiếp chắn nửa đ ờng tròn)= 2 BH . BA = BC %4'e1'"7C9'/ .1@: BH BC BHC BFD (g-g) BH . BD = BC . BF BF BD = ~ ã ã DCB BCE = ã ả 2 2 D E =  BH.(BA+BD) = BC.(BC + BF) BH . AD = BC . CF (1)⇒ ⇔ haF@:iiOS%j'/@'Nk  ¶ · · · 2 0 D CAB (so le trong) AH AC ACH DF BD mµ AHC DFB 90  ⇒ =  ⇒ ∆ ∆ ⇒ =   = =  ~ DBF (g- g) AH . BD = DF . AC (2)⇒ haF: AC CF ABC CDF (g -g) BC . CF = DF . AC (3) BC DF ∆ ∆ ⇒ = ⇒ ~ l%I%'%#9:HR<OR<HO $*9@:     + + + = + + +  ÷  ÷     1 1 21 3 21. 3. 21 3a b a b b a b a )N > , 0a b <m2(n>"o/#?"7p: + ≥ × = 3 3 21 2 21 6 7a a a a % + ≥ × = 21 21 3 2 3 6 7b b b b % _l'MA%'%"7p:     × + + × + ≥  ÷  ÷     1 1 21 3 12 7a b a b h: = = 12 7 144.7 1008 I = = 2 31 31 961 ⇒ > 12 7 31 ⇒     × + + × +  ÷  ÷     1 1 21 3 > 31a b a b %"2  . 2m m + 2 2 2 2 2 (4 2) 2.(4 2) .100 6 100 6 100 6 2m m + + 2 2 2 2 (4 2) 100 6 (100 6 2) - (100 6 2)m ="19,->F = = = 2 2 2 4 2 100 6 0 4 100 8 252m m m = = 6 7 6 7 m m -"eF42789!@4 P"@=W% T * +. =  +  2 2 2 2 10 5 1 1 (I) 20 3 11 1 y x y y x y `a = 2 x u % ≥ 0u ' = + 2 10 1 y v y R4%b9c: − = − = = =     ⇔ ⇔ ⇔     + = + = − = =     5 1 10 2 2 13 13. 11 5 1 4 u v u v u u u v u v u v v  )N = = = 2 1 1 1u x x )N = = = + = + = 2 2 2 10 4 4 4 10 4 0 1 1 2 y y v y y y y B.1>4%b"'N = = = 1 1; 2 hoặc 2 x y y <)^4%b@4%II%I 1 2 I%WII%WI 1 2 #*/1234.563/* +