¤n tËp häc k× 2 BÀI TẬP : ĐẠI SỐ Phần I: Bất Đẳng Thức Bài 1:  ≥ba            + ≥ + baba      bababa ++ ≥ + Bài 2: cba ≥≥     cbacba +−≥+−  ababcba   ≤+≤++  Bài 3:   ≥−−++ acabcba Bài 4: !"#$      ba baba a − ≥ ++         cba aacc c cbcb b baba a ++ ≥ ++ + ++ + ++ Bài 5: !"#$   %%  cbaab abcba ++ ≤ ++  abc abcacabccbabcba %%%%  ≤ ++ + ++ + ++ Bài 6:  % << x &'(&))*  % xxxf −=   > x &'(&))*    x xxf +=  % << x &'(&+)* %  xxxf −= Bài 7: !"#$,-  .%%% ≥       +       +       + a c c b b a  / ≥       +       +       + a c c b b a Bài 8:    =++ > %  cba cba ,-  0% % % % % % ≥       +       +       + cba  . %%% %%% ≥ −−− +++ cba cba Bài 9:    =+ > %  ba ba  &'(&+)*12  ba ab + By: BÙI NGỌC HOÀNG 1 &'(&))*12         + ba %% Bài 10:    =++ > %  cba cba &'(&))*12  cba ++ &'(&+)*12  /// +++++ cba &'(&))*12 % % % % % % + + + + + cba "&'(&+)*12 %%% + + + + + c c b b a a &'(&))*12 accbba + + + + +  %  %  % Bài 11:    ≤+ > %  ba ba &'(&))*12 ba ba +++ %% &'(&))*12 ab ab + % Bài 12:      =++ > % %%%  cba cba &'(&+)*12 accbba + + + + +  %  %  % Bài 13:34567"89:8,-;#$' 2 <=   =+++++− cabcabxcbax >:8? Bài 14: !"#$,-    cba ac c cc b ba a ++ ≥ + + + + +    ≥ + + + + + ba c ac b cb a  % % %      ≥ + + + + + ab ab b ba a " cba b ca a bc c ab ++≥++ @         cba ac c cb b ba a ++ ≥ + + + + + A  %%% cbaa c c b b a ++≥++ Bài 15: !"#$,-   acaccbcbbaba a c c b b a +−++−++−≥++ Phần II: Bất Phương Trình, Hệ Bất Phương Trình Bài 1:(B8=:2C5D& %%  −++≥+ mmxxm Bài 2:&'61=5D& 2=    ≥−+ +−+≥+ % %%  mx xxxxx Bài 3:&'615D& 2#$6#$ %%  −+≥+− xxxx %  ≤+ mx  By: BÙI NGỌC HOÀNG 2 Bài 4:(B35D& 2  %%  −−+−≥− xxxx  % <+−− xxx  E%  ≥−− xx "    % % < + − − xx @ 0%  ≥−−− xxx A  0E %  %  < +− − − xxx  E  ≤− xx Bài 5:&'&FG*38 ! 2  % %  %  − − − = x x y  0E .   +− −−− = xx xxx y Bài 6:&'618 !>36H Rx ∈  %%  ++++= mxmmxy Bài 7:&'61=5D& 2=     −+≤ ≤+− % 0/  mxmx xx       ≤+++− ≤+− 0 %/   mmxmx xx Bài 8:(B3D&85D& 2  0  =+−+ xxx    ≥+−− xxx    ≤+− xx " %% ≤+−+ xx @ xxx −≥−+ % A %  +−≤− xxxx  % −=−−+ xxx    +≤−− xxx   E   ≤ + − x x Bài 9:(B3D&85D&  %% =+−−++− xxxx  E%0  +≤−−− xxxx    ≥−+−+ xxxx " %%  +−≥−++ xxxx @ % <+++ xxxx A % %E %   ++ ≥++ xx xx Bài 10: &'61;#$' 2= %  =+−−− mxx &'615D& 2=   ≥+−+− mxxxx &'615D& 2=6I>27C;>36H %%  =+−−+−++− mxxxx Bài 11:&'615D& 2=6I> /  E %   < +− ++ ≤− xx mxx Bài 12:,->JK  0  >+−−−+ yxxyyx    ≥++++− yxyxyyxyx    >−−−−+++ xyzxzxyzyx By: BÙI NGỌC HOÀNG 3 BÀI TẬP :HÌNH HỌC B i 1:à LD&&MND&&O*" 1. "6P261,QRN&D Q0u = r 2. "6P261)QN&D&  Q%n = − r 3. "6P261D%QN= ! k = −  "6P2614RQN5%Q Bài 2: L;#$'6#ST" % "6P261*6#ST %    %E   %  d x y d x y− − = − + = 86 P2614Q  "6P261*6#ST %   E   E   d x y d x y− + = − + = 8  6#ST    d x y− + =  "6P261*6#ST %    E     d x y d x y− + = − − = 8 2<6#ST   / % d x y− − =  GP24Q89U8  0  Bài 3 L;#$'6#STdLdV3OxOy9ABW#S X; 2  EQM :8261AB  OAB ∆ 2<Y8dP2  QN −   OAB S ∆ = 8dP2  Q%  M    ÷    " 0 OAB S ∆ = 8d2<6#ST Z   % d x y− + = Bài 4: ABC ∆ L4QRE5%QRQR L;#$'[P23* % 59345  G#STP248  95  &22JL4,86#S4\&'67Y6#S\  G#S2]95 E G#S2'  945 0 G#S;Y34 Bài 5:    N %Qd x y M− + = % &'67'L2\*,:^"  &'6761)6!>*,P2" 3. L;#$'6#ST d ′ 6!>* d P2 M  Bài 6:F_H`#$6!*3a;6#ST 28'61*I L2  + + = + − = 1 2 : 2 3 1 0 & : 4 5 6 0d x y d x y  − + = − + + = 3 4 : 4 2 0 & : 8 2 1 0d x y d x y By: BÙI NGỌC HOÀNG 4   = + − − =  = − +  5 6 5 : & : 2 11 0 3 2 x t d d x y y t "  = + + − =  = −  7 8 5 : & : 5 0 1 x t d d x y y  @ = + − = 9 10 : 2 & : 2 4 0d x d x y Bài 7: 6#ST %      /       D x y D x my+ + = + − =  &'m61 %  D V   D  %    b b D D  %     D D⊥ Bài 8:&;67 ABC ∆ L4%Q%5QRQR % &` ABC S ∆   &'6761,276#STx-2y-1=0  %E ABC S ∆ = Bài 9:6#ST    x y∆ − − =    . x y ′ ∆ − + = % &'^c>61,3 ∆ 7dB  &`dB3e ∆ 8 ′ ∆ Bài 10: %    x y∆ + + =    0 x y∆ − + = % &`e % ∆ 8  ∆  L;#$'6#ST6P24%Q8X; % ∆   0   L;#$'6#ST   % ∆ 8dB36L  ∆  % Bài 11:&;674%QR%5%Q%QR % L;#$'6#STP24836f258 2. L;#$'6#ST ∆ P258dB3g6L ∆  Bài 12&'C;X;36136f26#ST % %   0 x y∆ − + = N     x y∆ − − =     0 x y∆ + + = N  E % x∆ − = ;Y39h  ∆ 8  ∆  Bài 13:6#ST : 3 2 1 0x y∆ + − = 8 : 5 3 +2=0d x y− % F_H`#$6!e6#ST^  &`dB3g4EQ6L6#ST ∆  L;#$'36#S;Y3*9h6#ST^  &'61,27 ∆  dB3g,6L " E E &'61)276#ST 1 ( ) : 2 0x y∆ − =  dB3g)6L ∆ :idB3g)6L "  Bài 14    '  '  8 ABCD   Y  QEI  8    9    ^ %   0 x y∆ + − = 8    E % x y∆ − − = L;#$'39j:9*' '8 By: BÙI NGỌC HOÀNG 5 . ¤n tËp häc k× 2 BÀI TẬP : ĐẠI SỐ Phần I: Bất Đẳng Thức Bài 1:  ≥ba            + ≥ + baba      bababa ++ ≥ + Bài 2:  cba ≥≥    . c c b b a a &'(&))* 12  accbba + + + + +  %  %  % Bài 11:    ≤+ > %  ba ba &'(&))* 12  ba ba +++ %% &'(&))* 12  ab ab + % Bài 12:       =++ > % %%%  cba cba &'(&+)* 12  accbba. xyzxzxyzyx By: BÙI NGỌC HOÀNG 3 BÀI TẬP :HÌNH HỌC B i 1:à LD&&MND&&O*" 1. "6P261,QRN&D Q0u = r 2. "6P261)QN&D& 