Bài tập Hệ phương trình đại số vô tỷ

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


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

 
 
 

!   '

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

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

 


! 
! 
6 67 7
7 67 6

− = +
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− = +
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= − − − ⋅   
   

 




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

 
 
 
! !  ! 
! !  ! 
6 7 7 6
7 6 6 7
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6 7
7 6
 + =
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+ =
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  
− ± − ± 
= ⋅   
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% 
 

 

6
7 6
7
6 7

+ =

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 + =

  ( ) ( ) ( ){ }   (  6 7 = ± ± ± ⋅∓ 

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

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


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

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


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

 


 

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

  

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

% 
 
 
&#
$
&#

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

 


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

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


 	


 
 
 
   ' $
 #  $ $
6 7 6 7
6 7 6 7

− + − =

+ + − =
  ( ) ( ) ( ){ } $$ ( 6 7 = − ⋅ 
 
 
 
  #
 '  
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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 !"		!"	
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()	*+	$*,)-.	/	%&001%1 
2345094
 

   
  

6 7 6 67
6 6 7 7

− = −

− = −
  ( ) ( )    
 
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
 + =

+ − − =
  ( ) ( ){ }  6 7 = ± ± ⋅ 
4'89:  !"2; ?4 @2A !"#B+-
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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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 !"		!"	
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()	*+	$*,)-.	/	%&001%1 
234504
 
 
 
  
  ' 
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 = 
 
 $
   
6 7 67
6 7

− − =

− − − =
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6 6 7 67 7
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% 
  
  
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!  
  
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7 7 6 7 6 7
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7 6 7 7 6 7
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6 7 6 7 67
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- 

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6 7 7 7
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6 7 6
6 7
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. 
 



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6 7
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0 

  
!   
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6 7 7 7 6 6 6 7
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!    ! 
 
  

6 7 6 6 7 6 6 7
6 7
6 7 6
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6 7
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7
6 6 7
6 7
6 7 6

− − =
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6 6 7 67
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6 6 6 6 7 7 6 7
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!  !   !   
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()	*+	$*,)-.	/	%&001%1 
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/ 62; <#=(DS62,3#:


 	


 
 



&
  ! 

6 7
6 6 7 6

+ =
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
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6 7
    
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 #    $
6 7 6 7
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67 6 7
6 7 6 7
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+ − − =
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∓ 

 	


 
 
 

  '
6 7
6 7 6 7

− =
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+ = −
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