Chuyên đề phương trình Toán 9

Vò V¨n Trµ- THCS Ph¹m Kha Ph©n lo¹i ph¬ng tr×nh
Bµi 1: Gi¶i ph¬ng tr×nh.
a/
x 5 3− =
b/
x 10 2− = −
c/
2x 1 5− =
d /
4 5x 12− =
e/
x 5 9+ =
f/
1 2x 10+ =
g/
2x 3 1 2+ = +
h/
3x 2 2 3− = −

k/
x 1 5 3+ = −
m/
3 x 1 8
15
7 x 5
+
=
−

n /
( ) ( )

7 x 8 x x 11− − = +

q /
( ) ( )
1 1
17 3 x 1 23 4 x 1
11 15
− − = − −
p/
2x 3
2
x 1
−
=
−
u/
2x 3
2
x 1
−
=
−

s/
4x 3
3
x 1
+
=
+

t /
4x 3
3
x 1
+
=
+

o /
x 5 1 x+ = −
i /
x 4 2 x− = −

¬/
x 4 4 x− = −
l /
x 13 x 1+ = +
y /
4 3 x 6 5x− + =
w /
3 2x 3 x+ − =
*/
2
x x 1 x 2+ + = +

m* /
2 3 x 3+ + =

Bµi 2: Gi¶i ph¬ng tr×nh:
a/

x 1 2− =
b/
2x 1 4− =

c/
2x 5 4− =
d/
3 7x 2− =

e*/
1 x 1 2
− − =
f/
( )
2
x 1 5− =
g/
2
x 8x 16 5− + =

h/
2
4x 20x 25 1− + =

k/
2
1 4x 4x 5− + =

m/
x 15 3x 1+ = −

n/
7 x 5x 1− = +

p/
5x 4 4 5x− = −

u /
2
x 5x 4 x 4− + = +


v/
2
x 10x 25 x 3− + = +

s /
2
25x 30x 9 x 7− + = +
t /
2
x 22x 121 2x 15− + = −

r/
2
9x 2x 1= +

z/
2
x 6x 9 3x 1+ + = −
w/

4
x 7=
i/
2
16x 3x 7= +
j/
2
1 9x 6x 2x 6+ − = +
y/
( )
2
2
x 1 x 21 x 13 0− + + − − =

Bµ 3: Gi¶i pt:
a/
2x 1 2x 1 4− + + =

b/
2 2
x x 5x 7x 1+ = + −
c/
2 2
2 3x 6 x 0− − − =
d/
x 1 2 x 2 3 x 3 4− − − + − =
e/
2 2
x 1 x 4 3− + − =

f/
5 x 2 x− =

g/
x x 1 2x 1 3+ − − − =

h/
2 2
x 2x 1 x 6x 9 4+ + + − + =
u*/
x 3 4 x 1 x 8 6 x 1 5
+ − − + + − − =

v*/
x 2 x 1 x 2 x 1 2+ − + − − =

Bµi 4: Gi¶i pt:
a/
5x 1 3x 2 x 1− − + = −
b/
x 2 2 x 0− + − =
c/
x 1 2 1 x− + = +

d/
x 4 x 4 2+ − − =

e/
x 7 x 1 4+ + + =
f/

3x 1 x 1 2+ − − =

g/
5 x x 3 2− + − =
h/
2x 1 x 3 4+ + − =

k/
x 6 2x 5 x 1+ = − − +
m/
x 4 x 1 2x 9+ + + = +

n/
6 2x 4x 3 3− + − =
l/
2x 3 x 1 1+ + + =

j /
x 2 x 1 2− − + =
Vũ Văn Trà- THCS Phạm Kha Phân loại phơng trình
s/
2
x 9 3 x 3 0 =

t/
2
x 4 2 x 2 0 =
u/
x x 1 1+ + =
o/

x 4 x 1 2+ + =
p/
2x 1 x 3 4+ + =

q/
x 1 5x 1 3x 2 =

w/
x 3 x 4 1+ =

Bài 5: Giải phơng trình:
a/
1
4x 20 x 5 9x 45 4
3
+ + + + =

b / 36x 36 9x 9 4x 4 16 x 1 =
c /
2 3x 4 3x 27 3 3x =

d/
3 2x 5 8x 7 18x 28 + =
e/
1
4x 20 x 5 9x 45 4
3
+ =

f/

16x 16 9x 9 4x 4 16 x 1+ + + + = +
Bài 6*: Giải pt:
a/
x 14
x 5 3
3 x 5

=
+

b/
( ) ( )
x x
5 2 6 5 2 6 10 + + =
c/
2 2
3x 2x 2 x x 1 x+ = + +
d/
2
x 4x 5 2 2x 3+ + = +

e/
2
x 2 x 1 0 =
g/
2 2
1 1
2
x 1 x x 1 x
+ =

+ + +

h/
4 2
x x 1993 1993+ + =

f /
x
8
x
2
x
2
2

x
2
1 x 1
=
+
+
+
+
+ +

( Vế trái có 100 dấu phân thức)
Bài 7: Giải phơng trình:
a/
2
4x 9 0 =

b/
3
x x 0 =

c/
2
8x 0,75 0,58 =
d/
2
2x 7x 0 =

e/
2
5
x 3380 0
9
=
f/
2
x x 0 =

g/
2
4x 3 0 =
h/
2
x 3x 0 =

k/
2

x 36 0 =
m/
2
3x 7x 0 + =
n /
2
x 20 0 =
l/
2
2x 13x 0+ =

u/
2
2x 12 0 =
v/
2
3x 8x 0 + =
t/
2
x 1 0+ =
q/
2
3x 14x 0 + =

p/
2
5x 0 =
r/
2
x 14x 0 =

s/
2
3x 10x 0 =
i/
2
2x 3 0+ =

j /
2
2x 72 0+ =
w /
2
2x 1072 0 =

ơ /
2
2x 3x 0 =
/
2
56x 1120 0 + =

z/
( ) ( )
x x 15 3 108 5x =

Bài 8: Giải pt:
a/
2
x 9x 14 0 + =

b/
2
x 4x 4 9 + =

c/
2 2
4x 4x 1 x + =
d/
2
x 4x 12 0 =
e/
2
x x 2 0 =
f/
2
4x 4x 3 0 =
g/
2
x 3x 10 0 =
h/
2
x 9x 36 0 =
k/
2
x x 20 0 =
m/
2
2x 11x 12 0 + =
n/
2

x x 1 0 + =
l/
2
3x 7x 5 0+ + =
s/
2
2x 13x 20 0+ + =
t/
2
3x 8x 4 0+ + =
o/
2
3x 14x 8 0 + =
p/
2
5x 6x 8 0 =
q/
2
x 14x 29 0 + =
r/
2
3x 10x 7 0 + =
z/
2
5x 9x 4 0+ + =
y/
2
3x 8x 4 0+ + =
1)
2

3x 14x 8 0 + =
2)
2
5x 6x 8 0 =
3)
( ) ( )
3x 1 1 x 15 + =

4)
2
x 2x 2 1 0 + =
5)
2
2x 7x 5 0+ + =

6)
2
0,7x 2,3x 3 0 =

7)
( )
2
x 1 2 x 2 0 + + =

Vò V¨n Trµ- THCS Ph¹m Kha Ph©n lo¹i ph¬ng tr×nh
8)
( )
2
x 2 2 3 1 x 3 2 0− − − =
9)

( )
2
x 2m 1 x 2m 0− + + =
10)
( )
2
x m n x mn 0− + + =

11)
( )
2
2m 3 x 2mx 3 0− − + =
12)
( )
2
x 2 1 2 x 4 3 2 0− + + + =

13)
( )
2
4x 2 1 3 x 3 0− + + =
14)
( ) ( )
2 2
5x 3 5x 3 x 3− − + = +

15)
( ) ( ) ( )
2 2
x 2 x 3 2 x 5

− − + = −
Bµi 9: Gi¶i pt:
1)
4 2
x 7x 12 0− + =

2)
4 2
x 18x 81 0− + =
3)
4 2
4x 5x 9 0− − =

4)
4 2
x x 1 0− + =
5)
4 2
2x 5x 7 0+ − =
6)
4 2
2x 5x 7 0+ − =
7/
4 2
1 1 1
x x 0
3 2 6
− + =
8/
( )

4 2
3x 2 3 x 2 0− − − =
9/
2
2
1
x 2 0
x
+ − =
10/
( )
( )
2
2
x 1 x x 1 x 1 0+ − − + + =
11/
4 2
2x 7x 5 0− − − =
12/
4 2
3x 11x 14 0+ − =
13/
( )
4 2
x 2 3 x 2 3 0− + + =
Bµi 10: Gi¶i pt:
a/
( )
2
x 1 4 0− − =

b/
( )
2
2x 3 16 0− − =
c/
( ) ( )
2 2
x 1 4 x 3 0
− − + =

d/
4 2 2
x 4x 4 16x 8x 1+ + = − +

e/
3 2
x 4x 8x 8 0− + − =

f/
( ) ( )
2
2 2
x x 4 x x 12 0+ + + − =
g/
( ) ( )
2 2
x x 1 x x 2 12 0− + − + − =
h/
2 2 2 2
x 12 x 14 x 18 x 16

7 9 13 11
− − − −
− = −

k*/
2
2
1 1 19
3 x 4 x
x x 4
   
+ = − +
 ÷  ÷
   
u/
5 2
x x 2x 2 0+ + + =

i/
( ) ( )
x 2 x 3 0− − =
Þ/
( ) ( ) ( )
x 1 x 2 x 3 0+ + − =

o/
( )
3
x 3 27− =

p/
3
x
8
x 1
 
=
 ÷
−
 
w*/
( )
2
2
x 3 x 0
− + =
z*/
( ) ( )
2 2
x 2y y 1 0+ + − =

y*/
2
x 2 x 1 0− − =
1)
4 3 2
x 2x 6x 2x 1 0+ − + + =

2)

( ) ( ) ( )
x x 1 x 2 x 3 3+ + + =

3)
2
x 4x 5 2 2x 3+ + = +

4)
3 2
x 3x 3x 1 0+ + + =

5)
4 2
x 4x x 2 0− + + =
6/
4 3
x x 3x 3 0− − + =
7/
( )
( )
2
2
2 2
2x 3x 4 x x 1 0− − − − =

8/
3 2
x 3x 3x 9 0− − + =
9*/
x 3 x 4 49

3 x 4 x 12
+ + + =

10*/
x x 1
2 0
x 1 x
+
+ + =
+
11/
( ) ( )
2
2 2
x 5x 30 x 5x 216 0− − − − =

12/
2
1 1
x 6 x 8 0
2 2
   
+ + + + =
 ÷  ÷
   
13/
( ) ( )
2 2
9 3x 2 4 7 2x 0+ − − =

14/
( )
( )
2
2
y 5y 8y y 5 84 0+ − + − =
15*/
( )
2 2
y 5 5 y 5 6− − − =

Vò V¨n Trµ- THCS Ph¹m Kha Ph©n lo¹i ph¬ng tr×nh
16*/
x 1 x 2 x 3 x 4
58 57 56 55
+ + + +
+ = +

17*/
( ) ( )
4 4
x 3 x 5 9+ + + =
18*/
[ ]
2
x 8 x 7 0− + =
19*/
4 2
x x 1993 1993+ + =

20*/
( ) ( )
2 2
x x 1 x x 12 12+ + + + =

Bµi 11: Gi¶i pt:
a/
x 4 2x 3
2
2x 3 x 4
+ −
+ =
− +
b/
( )
( )
2
1 1 1
x x 2 12
x 1
− =
+
+

c/
2 2
1 1
0
2x 1 2x 4
− =

− −

d/
( )
3 x 1
2x 1
6
x 1 x 1
−
+
+ =
− +

e/
x 4 2x 3
2
2x 3 x 4
+ −
+ =
− +
f/
1 1 1
x 1 x 9 x
+ =
− −

/
2 2 2
y 3 1
y 9 6y 2y y 3y

+ =
− + −

¬/
( ) ( )
3 2
32 1 1
x 2x x 2 x 1 x 2 x 1
+ =
− − − − − +

g/
2x 5 x
0
2x 2x 5
+
− =
+
h/
2 2
3 2
2
x x 5 x x 4
+ = −
+ − + −
h/
( )
2
x 1 x 2
x x 1 x x 1

+ +
=
− + +

k/
1 1 1
0
x 1 x 1 x 4
+ + =
− + −
m*/
3
3
1 1
x x
x x
+ = +

n*/
3
3
8
x x 2
x x
− − =
−
u*/
2 2
x 1 x 1 x 1 x 1
0

x 1 x 1 x 1 x 1
+ − + −
   
+ + + =
 ÷  ÷
− + − +
   


s/
2
14 4 x 7 1
x 9 3 x x 3 3 x
−
+ = −
− + + −
t/
x 1 x 1
3
x 1 x 1
+ −
+ =
− +

i/
2
y 2 y 2
5 6 0
y 1 y 1
   

+ +
− + =
 ÷  ÷
− −
   
j/
x 2 16x
7 0
2x x 2
+
− + =
+