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Bài tập Đại số lớp 9

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Z.

: E

a

b/

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a

1
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1
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:
a 1 a 2 a 1
1)

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: F


2
4).

1

a 1 a

a

x

x 2
:
x 1

1
2
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: K

x 2

2 x
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1
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2 x 9
x 5 x 6

1
2
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1; x 4).

x
x

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1
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x

x 1
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2 5 x
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4).

x 9
3 x 1
:
9 x
x 3 x
9).

x 3 2 x 1
x 2 3
x
4 ; x 9)

x 1
4 x :
x 1
1).

4

x 1
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x 2
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4).
= A 3 x + x.

a 2
a 1

:

a 2
a 3

c/
1
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b 3 1 1
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b
9)

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:
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2.
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a

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15 .

5
1
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a
4).

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1
x

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1
2 x
2
x x 4
4).

6
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5

1.
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: D

1
x


1
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1
:
x 1

1
:
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Z.

x 1
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1; x 9).

x 1
x 2
1).

x 3
x 1

x 2
x 1

:Q

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x 1
x 1

x 2
x 3
1.

x 1
4 x
x 1
1).

x

1
x

Q

Q.

x 1
x 1
3
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x 5 x 6
4; x 9).


:T


7 x 1
x 7 x

:

7 x 1
x 1
:
x 7 x x 49

x
x 4

M

2

1
:
x 2

x

2

x 2

10 x
x 2


4)
:

S

1 a2

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1 a a
1 a

a

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1 a

a

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x 1

x

1

1)
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: K


x x

x

x x 1
1
x
x 1

1
x
x 1
:
x 1
x x 1

1

:C

x 1

x

x

x 1 x 2 x 1
1)
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x 2
x 1

x 2
x 2 x 1
1).

1 x
2

:

2

B

x 2
x x 1

x
1
x 1
:
2
x 1 1
x
1)

x


2

L.
: E

x 2
:
2 x 2

x
x 2
2)

1
x 1

: H

x2

x

x 1 x

x 1

x 3
x 1


0)
:
1.

G

a 2
a 2 a 1

a 2
a 1

a 1 a 1

: N

a2
a 2a
a
1
a
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a
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1

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7
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y=

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c/ 3

2

t


2

a/

a/

9 4 5

5 3

2).

b/ 2 125 3 45
1

180 :

5

2
2).

1
3

c/

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35 6

2

4
3

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4

1

8 2 2
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4 6 2
2

3
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2

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8 2 7

2).

b/ 2 112 5 7 2 63 2 28
1

7

2
2).

1
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2
2).

1
3

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1

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7

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c/


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21

2 3 3 2
3
2

4

3
5
2 1 6

5

21 d/

5.

2

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1

y=

3x

1
2
1

4

b/

8 3 2

c/

6

14 6 5

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10

2

5

2
1

2).

3


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1

5)
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5

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d/

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2

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:
1

y=3
1

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b/

(D2).

1
3

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4

1

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2

2

5


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10

3 3 2 2
3
2
:

11 3 22

2 3
2
3

3

5
4

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6

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6 2 5

b/ 15 200 3 450 2 50 : 10


2).

1
3

1

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2

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1

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14 3 20

2

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1

x
y=
2

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3

c/

a/

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99

2

5 3

2

1

y=5

41 12 5

a/

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6
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11

5 1

a/

6
6
2

11
11

9 4 5

2).

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1

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2
2).


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4)

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5

5

1

6 2 5

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2

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song song (d1

3

3

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2

5


2

:
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1

y=

x
3

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12

3

23 4 15

2).
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48


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192 : 2 3

2
2).

1
3

c/ 2
1

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2
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5

1
5

1

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2

1

y=

x
4

a/

5

2

22 4 10

b/

27 6


1
3

21

3 8 2 7

2

2
7 3 5

2).
1

2
2).

1
3

2

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1


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2

1
1

2

3

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1
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5

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3

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2).

1

:

a/


8

c/

12

60

3

2

4

1

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2

b/ 42

60

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3
2
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1

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2

4

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c/ 4
2

3

7
7
3


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7
1
12

112

6
3

2

1

y=1

1
7

d/ 175

51 10 2

2

3

15
8

3

10 4 6

3

6

10

6

1

6 2 4
3 2

7

4

15


1:

2

2:
2

80m.
3

4m
2

195m2

5

4

m2
2x
x
x
2)
x
2x
3)
4x
2x
4)
5x
1)


y

8

y 2
2y 5
3 y 20
3 y 13
y 5
3y 6
2y
23

5)
5 x 2y
x 3y
6)

99

7 x 4 y 17

5x 2 5 y
5x

7)

3 x y


5

y 5

5

7y 7
3x
5 5 y 2x 0

x y
x 2y
3x 2 y
2)
x 2y
2x 3 y
3)
4x y
2x 3 y
4)
3x 5 y
1)

8
2
4
20
13
5
13

9

5)
3 x 2y
x 3y
6)

9

4 y 7x 5

2x 3 y
2x

7)

5 x y

y 2

2 2
4

3y 7
2x
5 3 y 2x 0

84m2
2


2x y 3
x y 6
3x 4 y 11
2)
5 x 6 y 20
1)

1
2
x y
3) 3
3
x 3y 2

4)
5)

3 x 5 y 11 0
5x 4 y 1 0
x y 2

6

2 2x 3 y 8
6)

2
4x

3 x 3y

y

2x
x
3x
2)
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3
x
3) 2
3x
1)

2 5 3

4 2 3

3y 1
4y 7
2y 8
3y
12
1
y
2
2y 1

4)

x y 4 x

3x 2 y
7

5)

3x 2y
x y 2

5

2 1 x y

2

6)
x

2 1 y 1

2
2

1)

2 x 11y
10 x 11y

7
31


4)

x

y

7x 3y

2 x 1
x

y 4

1)

2x y 2
9x 2 y 1

4)

sau:
2 x y

5 y

3x y 1 3 y 2


2)


x 0,5y 2
2x y 4

5)

5x

2

5)x

(1

2x 5 y 2
3) 2
x y 1
5

y

2)
y

2 1 x

1
3 y

2


2 1 y

2

2

6)
3 x

2

5)

2
3
x
y
3) 3
7
3x 2 y

5

2x 3y

3 2

x

2


y

x

6)

5y

0

5x 3 y 1

5

5

:
2

2

2:
1)

3 x 2 y 10
x 2y 4

4)


2)

5)

1
5
x
y
3) 6
14
5x 2 y 1

2

6)

2 x

y

11 y

3 x

y

31 8 y

2:
2 x 3 y 13

1)
4x y 5

x 3y

3

2)

2x y

2 3

4x 3y

2 2 3 3 1

2x y

2

3 3

2

x y 3
x y 9
2x 3y 2
2)
5x 2 y 3

1)

y x
6
4 5
3)
x y
0
15 12

4)

5)

5 x 2y

3x

y 2

2 2

1

2 x y

1

2 x


2x y

3x 2 y 1

x

5)

2y
x

x y
1
3) 2 3
5x 8 y 3

x
x
3x
2)
2x
1)

12

6

x

6


3y

3

3 1 y 1

6)
3 1 x y

y
3
y 13
2y
12
4y 8

4)

5)

3

2y
2,3
5
3)
3y
x
0,8

5

3
1

x 1 y 1

xy

x 2 y 1

xy

2x

y 3

4 3

3x 3 y

3x
4

6)
y

4y x 5

2


6 2

2x 2 y

x 3y 2 0
2x 6 y 1 0

x 3y

.

3x 1

2x 4 3 x 5 y

4)

6)

3 3 6

3x 2 2 y
2x 4 y

6 2
20

H


:
54

5
2

3

1)
x 3y 4
2)
3x 2 y 1
x 2
3) y 3
x y 10 0

4)

5)

2 x 3

1

3 x y 1

2 x 2

x 2 3y


2 2

2x
6)

3 y 1

y 2

3x 2 2 y
2x 3 3 y

x
3x
3x
2)
6x

1)

3

y 3
2y 5
2y
8
y 9

2x 3 y


4

3)

7
2 6

x
y

3
10

4)

5)

4

6)

3 x

y

9

2 x y

2 x


y

3 x y

3 5x y

6 5

x 4 5y

2

5 2 x y
x 2y

3

6 2 5

11

5


100
1

2
10m2.


1)

2)

3x
4
3)
5x
2
5)

7y
41
3
3y
11
5

x 2 3y
x 2y

x 2y 4 0
3 x 6 y 12 0

5 x 2y

4)

5


5
2

x y

3 x y

7 x y

3 5 x 4 y 15 2 7

6)

2x y 3
3x y 7
13 y
3x 10
2)
18 x 32 y 40

5)

3x 2 y
3x

6)

3


3y

2 3x 2

4 5 3y 2

4 3x 2

7 3y 2

3 2x 4 y

2
0

3x
x
2x
2) x
2
3)

2

,n
60m2

6)

y

x

12

2 x y
2y

11

5

2x y 1

10

3 x 1

5)

x

2y

2 2x y
6)

2

4 2


2 6x 9 y
2x

7 y 3

2

3y

5 3
5

0
12

5s 3t
3
4 s 3t
2

s t
t 1

,n
2m
42m2
2

5
4)


2x

3y 1

5)

5x y

5

x y x 1

x y x 1

2 xy

y x y 1

y x y 2

2 xy

x 2y 5
x y 4
3x 7 y 7
2)
2x 5 y
5
1)


5 2x 4 3 y 8

2 3x 3 5 y
3)

5 x

4021
4021

5 x y

hai

2

y 4
y
5
3y 1

y

3s 2t
5
4)
2 s 3t
3


2

y

3 x y

4)

4y 1
5y 4
3y 1

x 5 y x y 3

2x 1 y 2 1
4
3
12
4)
x 5 y 7
4
2
3

x
2x
2x
2)
x


2011x 2010 y
2010 x 2011 y

3)

x 2 2 3y 5
5)
9
3 2x
3y
2

1)

6

5x 3 2 y

1)

x

2 5 x 8 7 y 18

2 2

1)

3)


3 y 17

8m2

y 5
x y 13
3y
x 18
2)
y 10 5 x
1)

99

4

3 1
21

3)

x 3 2y 5
4x 1 3y 6

4)

2 2x 3 3 y
2x

6y


5

5 2

1

2 x

1

2 y

5

1

2 x

1

2 y

3

5)

2x 7 y 1
6x 1 2 y 3



2mx

1:
a/

hai ng

A

t x1, x2
A = x12

x 22 x12 x 2 x1x 22

(x1 x 2 ) 2 7
x1 x 2 1
11: Cho x2 4x + m

a/
1>

3x m

2:

x1
x2

x2


2
.
3

A

2

a/

1,

x2
a/

x13 x 32 27 .
3: Cho x2 (m 1)x m 2 = 0

x1, x2.

a/
x1, x2.

A

B
4:

5

x x x12 x22
12: Cho x2 mx + m
2 2
1 2

x12 4 x1 x2 x22
2x m2 + 4m

2 x1 x2 7 2 x1 2 x2
x12 x22 2 1 x1 x2
13: Cho x2

a/
t x1, x2

x12 x 22 4x1x 2 3

A x13 x 32
2mx 3m2 + 4m

5:

.

.
1)x

14:

m


a/

hai

m x1, x2

x1, x2

A
6: C

A x12 x2

x1 x 2
(2m + 1)x +

15: Cho x2 2x + m

a/
a/

x1, x2
2

:x

x1, x2.

7x1x 2 x12 x 22

(2m 1)x + m2 m

x12 x 22 x12 x 22 3x1x 2
.
16: Cho x2 (m + 2)x + m

a/
x1 ; x2

R.
2
1

= 6x1x2 x x
(m + 2)x m

b/
: Cho

2
2

x1, x2

a/

1, x2

.
b/

: x2

x1 x22 3x1 x2 1

A = x12 x 2 x1x 22
6x m2 + 8m 7 = 0

x x22
17: Cho 2(mx + 1) x2

1,

: Cho x

2

x2 sao

3
2

x x
(2m 1)x m2

6
x x1 x2 x22
18: Cho x(x 2m) = 2
2
1


x1, x2

0
x1, x 2 .

x1 , x 2

2
1

x1, x2

A

3
1

10

A

x13 x 32 = 0.

K

2
1

x


48
x 6 x1 x2
2
2


2mx

19:

: Cho x2 2mx + m2 m + 1 = 0

4m

a/

1,
2
1

20:

x2

a/
b/
x1, x2.

2
2


A x x x1 x2
(2m 1)x + m2
x1 ; x2 .

a/
2
1

x

b/
21:

2m 1 x2
(2m

A x1 x2 x1 x2
: Cho x2 (2m + 3)x + m2 + 3m + 2 = 0
.

8
x1 ; x2 .

a/
2
1

x
: Cho x2


b/

b/

2m 1 x2 8 17m 0

x1, x2

a/ Ch

R.

x1, x2
: Cho x2 4x + 5m2 + 2m 3 = 0

1x2 4x1 = 2.

23:
a/

3 x1 x2

x=-

.
b/
x13 x23 35 .
x1, x2
24: Cho 3(mx + 1) x2


x
: Cho x2 2(m

2
1

x

18
4 x1 x2

2
1

1,

x2 .

1,

x2 .

2
2

x

8=0


x

2
2

1)x + m2

x1 x 2
4m

1=0
1, x2.

x1x 2 x12 x 22

x22
: Cho x2

25: Cho x2 (m + 1)x m
x1, x2
P x12

x

: Cho x2 2(m + 4)x + m2

x1, x2

A


2
1

x1, x2

x22 x1 x2 3x1 3x2

A

2
1

x

9
x x1 x2 3
2
2

26: Cho x2
: Cho 2(mx + 1)

x1,
x2

x2
1,

2
1


x2

2
2

x x
27: Cho x2 (m 1)x + 2m
x1,

A

x12 4 x1 2 x22 4 x2 2

2 x12

x22

: Cho x2 4x + m = 0

x2
x1 x2 5
.
x2 x1 2
: Cho x2 2x + m 3 = 0

a/

3x1 2x2 = 7.
: Cho x2 2(2m + 1)x + 3m2 + 6m = 0

x2 .
3x1 x2

1,

A x12 x22

x12

x22

1,

2m 1 x2

x2 .
m2

: Cho x2 + 3x + m 1 = 0

x1 x

1

x12 x1 x22 x2 14 .
x1 = 2x2.
(2m 3)x + m2 2m + 1 = 0
c
x1, x2.
5x

=
16.
1
2
2x 2m2

x1, x2

a/
: Cho x2
x1, x2

1,
4
1

a/

: Cho x2

: Cho x2 + (2m 1)x + m2 = 0

A x12

x1, x2.

4
2

x2 32 x


1

x2 .
3

x12

4 x22 .


: Cho x2

: x2

a/

x1, x2.
4
1

a/

4
2

R.

x x 17 .
: Cho x2 2mx + m2 m


b/

x1; x2

x1 x2
: 4x + 2(3 2m)x + m2 3m + 2 = 0

x1, x2

2

x1 x2 8 .
: Cho x + 2mx 2m

a/
b/

2

.
2

:x
a/
b/

x1, x2

x1 x2


x22

2(m + 1)x + m + 3m

x12 x 22 x1x 2
: (m 1)x2 2(m

: x 2 2 2m 1 x 3m2 4 0

2=0
1, x2.

22
m 1)

a/

a/

1,

R.

x22 2 x1 x2 8 .
: x2 2(m 1)x 3 + m2

a/

1


nh nh t 3m

A=x1x2 + 2x1 + 2x2

1,

x2

320m2

4m

1:

= 0,

(3m 2)x
1 5x2 = 6.

50:

m.

b/

x 2.

b/
khi

c/

x1 ; x2

b/

x12

2

?
2

2:
3:
4:
5:
6:
7:

.
128m2
2

chu vi 140m

c

1176m


ao.
2

5/3
2/3
280m.

240m
150m2

2

8:

.000.
sau v
12:

286.650.000
?

?


a/ 2x

2

5x 7 = 0


c/ x 2

5 x

3

d/ 4x4

b/ x

15

2

4x 5 + 20 = 0

c/ x 2

0

12x2 + 9 = 0

2: Cho (P) : y =

1:
a/ 2x2 + 5x

1 2
x
4


1
x 2
2

(D) : y =

5 x

3

d/ 9x4

b/ x2 2x 5 + 5 = 0

7=0

15

12x2 + 4 = 0

2: Cho (P) : y =

3: Cho x2 2mx + m 2 = 0

x2
4

(D) : y =


1
x 2
2

3: Cho x2 3mx + 3m 2 = 0

.

a/

0

a/
x1, x2
x1 x2 , x1 x2 , x12

A=

2
1

x

m.
2
x2 theo m.

x1, x2
x1 x2 , x1 x2 , x12


24
x 6 x1 x2

A=

2
2

1:
a/ 4x2 + 9x = 0
c/ x2 + x = 12

b/ 2y 8 = 0
d/ 3x2 2x 6 + 2 = 0

2

f/ x 2

5 x

1

4

5 x

10
5


x

3 1 x 4

4

2

x2
.
2

.
mx + m 1 = 0
m.

3x2

x2
(P) : y =
.
4

2: a/

2

3:

.

x 1,

0

3
4

g/ 3x 2x 20 = 2x
4
x2 x 2
h/
x 1
x 1 x 2

(P) : y =

a/
x2

2 x 2 6

2 3

f/ 5 x 2

0

g/ x 3x = 2
x2 2 x x 5
h/

5
3
6

3: Cho x2

b/ 3x2 + 5x + 1 = 0
d/ 3x2 2(x 3 + 1) = 0

e/ x 2

0

2

2: a/

24
x 6 x1 x2
2
2

1:
a/ 2x2 3x = 0
c/ (x + 2)2 = 4 x

2

e/ x 2


2
1

m.
x theo m.
2
2

2.
2mx + 2m 1 = 0

.
1,

x2

theo m.

theo m.

A = x1x 2 x12 x 22

.

A = x1x 2 x12 x 22

1:
3 2
x + 27x = 0
8

c/ 9x2 = 4(3x 1)

b/ 4a4 9a2 = 0

a/

e/ x

2

d/ x2 +

2

3 x 2 3

5 = x 2

1:
3 x2 = 0
a/ 2 x3
c/ (x 3)2 = 10 4x
e/ x 2

0
f/

6 x2

b/ 9t4 4 = 0

d/ x2 = 2(3 + x 3 )

3 3 2 x 3 6
5 3 6 x

0

4 6 5


2 x2

f/ 5

g/ 3x2 + 7 = 4x4
3
2
h/
1
x 2 x 3

2 x 10 0

5

g/ 9x4 + 8x2 1 = 0
x
10 2 x
h/
x 2 x2 2x


2: a/

2: a/

x2
v (D) : y = 3x + 5.
4

(P) : y =

1
(P) : y = x 2
2

(D) : y = x + 4.

.
.

.
2

3:

.

(m + 2)x + m + 1 = 0

.


3: Cho x2 2x m2 1 = 0

1,

x2

x1 , x 2
theo m.

theo m.
1
x1

c/

x12

1
x2

2.
1(x1

1:
a/ 4b2 5b = 0
c/ x2 + 2x 63 = 0
e/ x

2


2) + x2(x2 2)

1:
a/ 2c2 5 = 0

2

b/ 3x x 2 = 0
d/ 7x2 + 1 = 2x 7

3

f/ 9 x 2 2 5

6 x 3 2

f/ x 2

3 x 2 3 1 0

g/ (2x2 1)2 = x2 + 2(x4 1)
x 5
2
h/
2
x 2 x 3
x2
2: Cho (P) : y =
(D) : y = x 1

4
(P).
.
3: Cho x2 + mx + 2m 4 = 0
a/ C

b/ 2x2 x 3 = 0

c/ 3x2 = 21 2x
e/ 3x 2

0

x22 3x1x2 = 1.
10
2
x1 x2 2 1

d/ x2
6 1 x

6 3 x

5x + 4 + 2 =0
2

6 4

g/ 3(x4 + 1) = 10x2
14

1
h/ 2
1
x 9
3 x
1
2: Cho (P) : y = x 2
(D) : y =
4

1
x + 2.
2

a/
b/
A(2 ; 1).
1,

x2 + mx + m

3: Cho

x2

1=0

a/ C

1,


x2

theo m.
i m = 1.
theo m.
c/

.
e/

x12 x 2 x1x 22

x1 2x1x2 + x2 = 5.

1:
a/ 7x

4

2

42x = 0
2

c/ 2(3x + 4) = 5x
e/ 2 x

2


2

b/ x

d/ 6x

1 2 2 x

8 =0

3
2

2x 3

2

0

1=0

1:
a/ 36x4 49 = 0
c/ 1 = 2x(2x 1)

b/ 2x2 3 6x = 0
d/ 5x2 3(2x 5 3) = 0

e/ x 2 4 5


21

5 x


f/ 1

2 x2

2 x

f/ 2

2

2

4

2

g/ (5x + 2) = 3(10x + 1)
16
30
h/
3
x 3 1 x
x2
(P) : y =
3


2:
.

(D)
M.
2

3:

5 x2

x

5 1

0

2

g/ x 29x + 100 = 0
x x 7
x x 4
h/
1
3
2
3
2:
(D) song

x
x2
song (d): y =
(P) : y
.
1
2
2
3: Cho x2 2mx + m 2 = 0
.

3mx + 3m 4 = 0
x1, x2.
b/
theo m.
c/
x1, x2

x1, x2
theo m.
c/
d/

1

x2 theo m.

x12

x 22 5x1x 2 18

24

d/

2

1:
a/ 2x2 2x = 0
c/ x2 = 6(x 1)

1:
4

18 = 0
b/ x 2
2
d/ 4x 4x 5 + 5 = 0

e/ x 2 2
f/

3 1 x 4 3

5 1 x2 2 5x

5 1

f/

1.


2

3:

.

theo m.

d/
x1, x2 th

x12 x 22 x1x 2

2

1:
a/ 25x

2

2.
(2m 1)x m = 0

b/ 16x4 25x2 = 0
3 ) = 11
d/ 2x(x

a/ x 3 6 2 x = 0
c/ 2x2 + 5x 1 = 0

e/ 4 x 2 2

a/
b/
M

2

0

g/ 3(x2 + 18) = x4
12
8
h/
1
x 1 x 1
x2
1
2: Cho (P) : y =
(d) : y = x
4
3

a/
x1, x2

x2 2 6 x1 x2

x1


.

3 1 x

3 2 x2

5

3

0

3 x

5 2 0

g/ 5(x4 1) = 24x2
x 2
6
h/
3
x 5
2 x
x2
2: Cho (P) : y =
(D) : y = x + 1.
4
a/
.
b/

-4.
2
3:
ng
+ (2m 1)x + 3m 4 = 0
.
a/
x1, x2
.
theo m.
c/
x1, x2
d/

x12 x 22 x1x 2

5

1:
a/
7=0
b/ x4 + 11x2 = 0
1
3
b/
x=0
2
4
c/ 4x2 5(4x 5) = 0
d/ x2 2 2 = 2x 3

d/ 3 x2 6x + 5 2 = 0
3x 2 3 4 0
e/ x 2

16 = 0

c/ 3(x2 + 4) + 5x = 0
3x
e/ x 2

2

6


f/ 1
4

2 x2 2 1

2 x 1 3 2

f/ x 2 2

0

2

g/ x = 8(x + 6)
x 3 x 3

h/
3
x2
2: Cho (P) : y =
2

2

g/ 3x (3x + 2) + 1 = 0
2
1
4 x
h/ 2
2
x 4 x 2 x x2 2 x
x2
2: Cho (P) : y =
4

x 1 x

2

2 1 x 1 2 2

a/

a/
b/ Cho A


2.

-2.
(4m + 1)x + 2(m 4) = 0

:
(m + 5)x m

a/
b/
c/

1
x
3
.

-3.
B

i (P).
3: Cho

0

2

1,

1,

2
1

x x 2 x1x

x2 theo m.

i m = 1.

x2
ph

1, x2

2
2

1,

x1 x2

2

65 .

x2 theo m.




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