Giáo án lớp 12 môn Toán - Bài 6: Hệ phương trình đại số vô tỷ

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Giáo án lớp 12 môn Toán - Bài 6: Hệ phương trình đại số vô tỷ
	

		 
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6 7 6 7
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    ± ± 
= ⋅       
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6 7
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7 6
6 7
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6 7 6 7 6 7
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+ + =  
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6 7
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6 7 67
6 7
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 ! ! 
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7 6
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7 6
7
6 7
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+ =
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! !   & 
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# #  
6 7
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= ⋅      
      

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6 7
7 6
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6 7
7 6
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6 7
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
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7 7 6
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7 6
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
+ + − =
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= ⋅  
  

% 
 
 
  
  
6 7 7 6
6 6 7 7
 + + + =

+ + + =
  ( )     
 
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  
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    


 
  
  
! ! 
! ! 
6 6 7 6 7
7 7 6 7 6
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− − = −
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! !  
! !  
6 7 67 6
6 7 67 7
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6 7
 
   
− − 
= ⋅       
    
 

 
 
 
# !   
# !   
6 7 6
7 6 7
 + = − −

+ = − +
  ( ) ( )    )6 7 = ± ± 
 
 
 
  #
  
6 6 7 6 7 6 7 7
6 6 7 6 7 6 7 7
 + + + + + + + + + =
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  ( ) ( )  )6 7 = 
 

 


 

6
7 6
7
7 6
 
− = 
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" 
 
 

  

  
6
6 7
7
6 7
  
+ =   +  
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− =   + 
  ( ) ( )     
 
6 7
  
= − ⋅  
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% 
 
 
&#
$
&#

7
6
6 7
6
7
6 7

+ =
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6 6 7 6 67
7 6 7 7 67
 + − + − − = +

+ − + − − = −
  ( ) ( )   )6 7 = − 
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  #
6 67
6 67 7
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6 67 7
6 67 7
 + + =

+ + =
  ( )  & # & 
& &
6 7
   
= ± ⋅   
   
∓ 
 
 
 
 
  
6 67 7
6 67 7

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+ − =
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  '
   $
6 67 7
6 67 7

− + =

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6 7
   
= ± ± ± ± ⋅  
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" 
 
 
  
  &
6 67 7
6 67 7
 + + =

+ + =
  ( ) ( )       
 
6 7
   
= ± ± ± ⋅   
   
∓ 
% 
 
 
  '
   #
6 67 7
6 67 7

− + =

− + =
  ( ) ( )     $  
 
6 7
   
= ± ± ± ⋅   
   


 	


 
 
 
   ' $
 #  $ $
6 7 6 7
6 7 6 7

− + − =

+ + − =
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  #
 '  
6 67 7
6 67 7
 + − =

− − =
  ( ) ( ) ( ){ }   ( 6 7 = − − ⋅ 
 
 
 
 !  
 
6 6 7 7 7
6 67 7 6 7

− − + =

+ − = −
  ( ) ( ) ( ) &  $$    
  
6 7
  
= ± ⋅  
  

 
 
 
     $
 #    $
6 7 6 7
6 7 6 7

− − + − =

+ + − + =
  ( ) ( ) ( ){ }   (  6 7 = − ⋅ 


 	


 


  &
  
6 67 7
6 6 7

− + =

− + =
  ( )        
& '
  ± − 
⋅   
   
∓

 
  
& 
$ 
67 6 7
6 7 7
 = + +

= −
  ( ) ( )     

6 7
  
= − − ⋅  
  

 
 
  
 !  
 
6 7 6 6
6 6 7
 + + =

− =
  ( ) ( ) ( ) ( ){ } $$     6 7 = ⋅ 
 
 

! !   
!  
6 7 7 6 6 6
6 7 6
 + + + = − +

+ + =
  ( ) ( )     

6 7
  
= − − − ⋅  
  

" 
   

  '
  
6 6 7 6 7 6
6 67 6
 + + = +

+ = +
  ( ) & 
6 7
 
= − ⋅ 
 

% 




!  
6 7
7 6 6

− + =

 + − + = −

  ( )  
6 7
 
= − ⋅ 
 


 	


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6 7 6 67
6 6 7 7

− = −
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− = −
  ( ) ( )    
 
6 7
  
= − ⋅  
  

 
  

6 7 67
6 7 6 7
 + − =

+ = +
  ( ) ( ) ( ) ( )
 
 
 $   $    
 
6 7
 
= ⋅ 
 

 
 
 
 
   '
6 7 6 7
6 67 7

− = +

− + = −
  ( ) ( ) ( ){ }    6 7 = − − ⋅ 
 
 
  

 
6 7
6 7 67 7
 + =

+ + =
  ( )  
 
    
  ( 
  
6 7
    
= ⋅         

" 
 
 
# 
 
6 6 7 7
6 7

− = +

− =
  ( )      
 
 
± − ⋅ 
 
 

% 
 
 
 
 ! 
6 7 7 6
7 6
 + = +

+ = +
  ( ) ( ) ( ) ( ){ } $       6 7 = ± − − ⋅ 

 
 
 
 ' ! ! 

6 7 6 7 67
6 67 7

− = − +

− + =
  ( ){ }!    6 7 = ± ± ⋅ 
 
 
! !  6 7 6 7
7 7 6
 + + =

+ =
  ( ) ( ) ( ){ }   (   6 7 = − ⋅ 
 
 
  

! !   
6 7
6 7 6 7 67 7
 + =

+ − − =
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6 67 7
6 67 7 6 7
 + + =

− − = − +
 HIJ.K&LM  ( ) ( ) ( ) ( ){ }        6 7 = ± ± − − ⋅ 
 
   
 $
  $
67 6
6 6 7 6 7 67 7
 + − =

− + + − − =
 HNJ.K&.M  ( ) ( )    (  

6 7
  
− ± 
= ± ⋅   
   

 
  
  
  !  $
!   ! 
6 7 67 7 6 7
67 6 7 6 7

− + − + =

+ + = +
 HOJ.K&&M  ( ) ( )      ( 
 
6 7
   
= ± ± ± ± ⋅   
   

 
 
 
 $
 &  $
7 67 6
6 67 7 6 7
 + − =

− − + + + =
  
( ) ( )
 &
 & 

  (  
 
−
− ± 
 
⋅ 

− −
∓

" 
 
 
  
6 67 7 6 7
6 7 6 7
 + − = − −

+ + + =
  ( ) ( )   ( 
 
6 7
  
= − − ⋅  
  

% 

 
  
   '
6 6 67 7
6 7 67 7
 + − = −

− + =
  ( )     ' (  ( 
  
− ±   
− − ⋅         


 
  
 
 
 
6 6 7 67 7 6 7
6 67 6
 + − = − −

− + =
  ( ) ( )  &   ( $ &

6 7
  ± 
= − ± ⋅   
   

 
  
 
 # $
  #  $
6 67 67 7
6 6 7

− − + =

+ − + =
  ( )   '  '  ( 
 
6 7
    ± ± 
= ⋅         

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  ' 
6 6 6 7 67
7 67 6 6 7

− + + = +

− − + =
  ( ) ( ) ( )   ( ' (   ( 
 
  
− − − ⋅  
  


 	


 
 
   
67 6 7 6 7
6 7 7 6 6 7
 + + = −

− − = −
 HNJ.KKPM  ( ) ( ){ }  6 7 = ⋅ 
 
   

 & & #
    
7 67 7 6 6
7 6 6

− + = − + +

+ − − = +
  { }!   ! (! 6 7 = − ⋅ 
 
 

6 7 6 7 6 7
6 7
 + + − = + −

+ =
  ( ) ( ) $ )6 7 = 
 
 $
   
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6 7 6 67 6 6
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 + − + + + =

+ + + = −
  ( ) ( )  )6 7 = 
 

 

 

!  

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6 7
6
6
6 6 7 67
7 6
6 7

− + =
+

− −
− =
 +
  ( )    
  
6 7
 
 = − − − ⋅
 
− 

Z Q,-ZQR@'X "9!6F'7 TE
 
 
 
  
  
6 7 6 7
6 7 6 7
 + + + + + =

+ + + − − =
  ( ) &  &    
 $ $
6 7
    
= ⋅    
    

 
  
    
6 7
6 7
 + =

+ + + =
  ( ) ( )   )6 7 = 
 
 
   
  &
  
6 7 7 6 67
6 6 7 7 6 7
 + + + =

+ + + = + +
  ( )     $   
  
6 7
    
= ⋅         

 

 



  
$

6
6 7
7
7
6 7
6 6

+ + + =


 + + =
 + +
  ( ) ( ) $  )6 7 = − 
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#
!  
6 7 67 7
67 7 67 6 7
 + + + =

+ + + =
 
( ) ( ) ( ) ( )
( ) ( )
      &  
 &
    

6 7
6 7

= − ±


⋅ ± = ±  
   

 

  
 
!  '
6 67 7
6 6 7 6 7 67 7
 + + =

+ + + + + =
  ( ) ( )     )6 7 = ± ± ± 
 

 



 

7
6 67 7 6
6
7
6 7
6

+ + + + = +

 + + =
 +
  ( ) ( )  &  &$  $  
  ± ± ± 
⋅   
   
∓

 

  
  $
# $
7 6 67 7
7 6 7 6 7 6
 + + − + =

− + + =
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6 67 7 7
6 6 7 6 6
 + + = −

+ = − +
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6 7
 
− ±
= ⋅ 
 
 
∓

% 


 
 
'

!  ! 
6 67
676
6 6
 + =


= +
− −
  ( )    

6 7
 
− ±
= ⋅ 
 
 

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6 7 6 7
6 7 6 7
 + + + =

+ + + =
  ( )   '  

6 7
 
−
= − ⋅ 
 
 

www.VNMATH.com
	

		 
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   # 
6 7 6 7
6 7 6
 + − + =

+ − + =
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6 7
 
= ⋅ 
 

 
! !     $
   
6 7 6 7 6 7
6 7
 − + + + − + =

+ + − =
  ( )   

6 7
 
= ⋅ 
 

 

 

 #
6 6 7
7
6 7
7

+ + + − =


 + + =


  ( ) ( ) ( ){ } $  $     ± − ⋅∓ 
" 

   

!   
6 7 67 6
6 6 7 7 7 6
 + = +

− + = +
  ( ) ( )   )6 7 = 
% 
 
! ! !  
   $
6 7 6 7
6 7 6 7
 − − + − =

+ − − − =
  ( ) ( ) ( ){ }     6 7 = ⋅ 

 
 
  
! !  
!   !  
6 6 7 7
6 7 7 6 6
 + + =

+ + + + =
  ( )     
 
6 7
 
− ± − ±
= ⋅ 
 
 

 

 
 !   '
6 7
6 6 7 6 7
 + − =

+ + + + − =
  ( ) ( ) ( ){ } &  $6 7 = ⋅ 
 
 

 ' #

'  
76
7 6
7 6
6 7
6 7
  
− − =   
  


+ + + =

  ( )   
' 
6 7
 
= ⋅ 
 

, 
 

  
 
67 6 7
6 6 7 7
 + + =

 + = + +
  ( ) ( ) ( ){ }    6 7 = − − ⋅ 
- 
 
 

 

76
7 6
67 6 7
   
 + =   
+ +   

+ = +
  ( ) ( ) ( ){ }  $  $6 7 = ⋅ 
. 
 
 
  

 
76
7 6 67 6 7
7 6 67 76
6 7 67

+ − = + −


− + + =
 + +
  ( ) ( )  )6 7 = 
/ 
  
 
   ) '
)  ) 
6 6 7 7
6 7 6 7

− + − = −

+ + =
 
   
!     
 
6 7
     
= ± ± ⋅       
     

 
! 
 
!    
6
6 7
6 7
6 7 6 7 6 7
 −
+ − + = +
 + − + = + −

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