Câu Lạc Bộ Yêu Toán Lý
________________________________________________________________________________________________________________________________________________________________________________________________________________________





2016 y  7 1  9x 2  1  2017  3x  1 y  1  2016 6x




9
3
 6x   20   9y 
 16   2016
y
xy




Biên Soạn: Nguyễn Minh Thành – Nguyễn Tuấn Thành
________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

1


Câu Lạc Bộ Yêu Toán Lý

x
x


1
8x 2  1



x

1
3

x2

x  1   3x  9  2x  3  4x 2  10x  4

x 3  6x 2  18x  10  2  x  1 2x  1

4x 2  5x  4   x  1 6x  1   x  3 2x 2  12x  1

6) (NMT)

1  x 

7) (Mathlinks)

1  x  1  x  1  x  1 


13) (NMT)

x



3





4  x2



x  x 2 1  2  x 2  x  x



2

x 3  3x  13  x  1  x 2  2x  3  2x 2  1

________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

2


19) (NMT)





x  2x 3  x 2  4x  2  x 2  3x  4

20) (NMT)

2

21) (NMT)

2  9x  2 2x 2  x  3 

22) (NMT)

x  1  x 2  2x  1  3 x 3  2x 2  5x  2

23)

24) (NTT)

x2
2  x 4  x 2  1  1



4


3
3
2
2
18 2  x  y   12 3 3  x  y  x  4x  2   17y  55

________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

3


Câu Lạc Bộ Yêu Toán Lý
________________________________________________________________________________________________________________________________________________________________________________________________________________________

3) (NMT)

4)





x 2   y  5 x 2  1  1  y  3


 4x 2  1  x  1  y  3


4
xy
 x  y  4 x  1  y  1  x  y  x  1  6

6) (NMT)


x y  x  2  y 1
 y  x  2 1 
x x


3
3
2
 y  x  2  2 x  3x  4  3x  2x  x

7)

8) (NTT)

9)





 y
x
y4


 2
4
4
 xy  3xy  2   xy  x  2y   1

10) (NMT)

 xy  4y  4  4  x  y  1 y  1

 xy  y  1  2 1  x

11) (NMT)

  x  y 2  5x  4y  13  x  2  2 y  1


 3 y  5  y  2  1  x 2

12) (NMT)
________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

4


Câu Lạc Bộ Yêu Toán Lý
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
4x  4x y  2x  8xy  y  2y  3  0

15) (NMT)

 y  1  2  2x  1 x  y   x  y  2

5x  4  2 3x  2  y  1

16) (NMT)

 x  2y  2y  1  2


 x  2y  1  2 2xy  x  4  x  2y  1  8y  x  1

17) (NMT)

 2
xy2
x 1

 x  2x 
2
y 1
y2  1

 x y  3  y  1 x  4  2  x 3 y  1  2x  x 2
 


20) (NMT)

 x  x 2  2  x  y  xy 2  4x  x  1  16


2
 x 6x  3y  4 2xy  8 2x  4x 2  y 2   16 2x x  y x  1


21) (NMT)

2y 2   x  12  4y x  2  7


1
x  y3

2

x

1

y

1

1
x


Câu Lạc Bộ Yêu Toán Lý
________________________________________________________________________________________________________________________________________________________________________________________________________________________



22) (NMT)

 

 xy  3 x  y  2  x  4 x  3

 2 1 
1
 x   1 xy  1  1 
x 
x




23)

 x 2  y3  y 2  2 3 x 4  3 x 2  2y y  1 x  3 x


3
 x 4  x 3  x 2  1  x  y  1  1

24)






2016 y  7 1  9x 2  1  2017  3x  1 y  1  2016 6x




9
3
 6x   20   9y 
 16   2016
y
xy




Hình học phẳng Oxy
1) (NMT)

 21 13 
K ; 
 10 10 
y40

(I;R).

M(0;4)


5)

x 1

 17 59 
I ; 
9 9 

4x  7y  57  0

yA  yD .

D  3;1

6)

N  6; 4 
2x  y  1  0

x  5y  0
7)

 25 19 
 13 19 
E  ;   HC  A 'B', F  ;   CI  AB . M  2;3
 7 7
7 7
xA  xB .
3x  y  3  0 ,

 x  2y  3 x  y
1
P   x  y  2 2 
 1 

 2y  4
y 1
x 1
 x  y 1 



x 1  y 1



________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

7


Câu Lạc Bộ Yêu Toán Lý
________________________________________________________________________________________________________________________________________________________________________________________________________________________

x 2  y2  z2  5 .

3) (NMT) Cho x, y, z


2 10

x 2  y 2  z 2  2x .

5) (NMT) Cho x, y, z

x 2  y 2  xz 

2z  x  y 

 x 
P
 2
 15 
2
2
2
 x  1 y  1 x   y  xz  x  y  xz  1  x  1 
a 2  b 2  bc  c 2 .

6) (NMT) Cho a, b, c

P  a 2  2a 





4c 1  ab  1  abc
a


y  z 1 x  z 1  z 

9) Cho a, b

2

2

a 2  b 2  1  3b .

 1  b2 
b2
1
P4



a 1 a  b  1 a2 

2

10) Cho a, b, c  1 .
________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

8



2
a b b c 
c






2

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________________________________________________________________________________________________________________________________________________________________________________________________________________________

Nguyễn Minh Thành – Sư Phạm Toán, Nguyễn Tuấn Thành – CS

9