11.Mot vai bai toan PT

Biên soạn : GV Nguyễn Trung Đăng
Vài bài toán phơng trình
1. Giải và biện luận các phơng trình sau
1)
( ) ( )
2
1 2 1 1 0m x m x m
+ + =
2)
( ) ( )
2 1 3 0x m mx m x
+ + =
3)
1 2x mx+ =
4) (m - 2)x
2
- 2(m + 1)x + m = 0 5) (m
2
- 4)x
2
+ 2(m + 2)x + 1 = 0 6)(m
3
- 4m)x
2
+ 2(m - 2)x + 1 = 0
7)1 +
=

ax
a4
ax2

x3

8)
5
7
mx
x
mx
m
=
+


9)
22
2
ax
a8
ax
a2
ax
x

=
+


10)
22
22

ax
ba
ax
bax
ax
bax

+


+
=
+
++
11)
2
ax
b
bx
a
=

+

12)
xba
1
x
1
b

1
a
1
++
=++
13)
ba
ba
ba
ba
x
1
x

+
+
+

=+
14) x
3
- k(x - 1) - 1 = 0
15) x
2
+ mx + m = 0.
16) (a
2
+ a + 1)x
2
+ (2a - 3)x + a - 5 = 0. 17) x

2
- 6ax + 2 - 2a + 9a
2
= 0. 18) x
2
- 2x + 1 - a
2
= 0.
19) (m - 1)x
2
- (2m - 1)x + m + 5 = 0. 20) (2 - a)x
2
- 3ax + 2a = 0. 21) (k + 1)x
2
- kx + 1 = 0.
22) ax
2
+ x + 1 = 0. 23) (m
2
- 1)x
2
+ 2(m - 1)x + 1 = 0. 24) m(m + 2)x
2
+ 2(m - 1)x + 1 = 0.
25) (a
2
- 5a + 4)x
2
+ (a -4)x + 4 = 0. 26) (m
2

- 4)x
2
+ (m + 2)x + 1 = 0. 27) (m
2
- 3m + 2)x
2
+2(m - 1)x +1 = 0
28) (m
2
- 5m + 6)x
2
+ (m - 3)x + 1 = 0 29)
2 3
0
2
x a
x a

=
+
30) (a - 1)x
2
- 2x - a = 0. 31) mx
2
- 4x - 3m + 1 = 0.
32)
0
a a
x a x a
+ =

+
. 33)
1 3 1
.
2 3x a x a
+ =
+
34) (a - 1)x
2
- 2x - a = 0 35)x
2
+ mx + 1 = 0. 36)(x - 3a)(x - a - 3) = 0
37) x
2
- (m + 1)x + 3m - 5 = 0 38) (2m + 1)x
2
- 4x - 2m + 1 = 0 39) mx
2
+ (3 - m)x + 1 = 0 40)x
2
- 6ax + 2 - 2a + 9a
2
= 0
41) 2(m - 1)x
2
- 4x + m = 0.
2. Giải các PT sau
1.
x96x10
=+

2.
3x27x9x3
2
=+
3.
85x39x
=++
5.
5x35x12x7
2
=+
6.
2
3x
1x2x1x2x
+
=+
7.
24x4x4x4x
=++
8.
15x9x8x
2
=++
9.
1x4x1
=+
11.
5x22x3x
2

=+
12.
x4xx3
2
=
13.
1x2
1x2
1x3
2
=


14.
3x1x24x3
+=++
15. x
2
+ 9 = 6x + 4
6x6x
2
+
16. x
2
+ 3 -
)4x(
2
3
2x3x2
2

+=+
17.
0xx27x12x6
22
=++
18. (x - 3)
2
+ 3x - 22 =
7x3x
2
+
19. (x - 3)(x + 1) +4(x - 3)
3x
1x

+
= -3
20. x
2
+ 2
4x31x3x
2
+=+
21. -x
2
+ 2x + 4
10)1x)(3x(
=+
22.
3)x6)(x3(x6x3

=++++
23. (x + 4)(x + 1) -3
62x5x
2
=++
24.
36x3x3x3x
22
=+++
25.
x9xx9x
2
+=+
26. 3
5x6x22x3x
23 2
+=+
27.
21xx1xx
2
4
2
=++
28. x +

2x17.xx17
22
=+
29. x.
30)x35x(x35

3 33
=+
30.
2)x3)(x1(x3x1
=++++
31.
3
2
3
2
3
2
)1x(6)1x(4)1x(
=++
1.

Biªn so¹n : GV NguyÔn Trung §¨ng
32.
1
x
)1x(2
1x
x2
=
+
+
+
33.
22
xx271x10x5

−−=++
34. 2(x - 1)
1x2x1x2x
22
−−=−+
35. (x - 2)
2x3x1x
22
+−=+
36. (4x - 1)
1x2x21x
22
++=+
37. 5
2
x2
1
x2
x2
5
x
++=+
38. 3x
2
- x + 48 = (3x -10).
15x
2
+
39.
5

2x
1x2
4
1x2
2x
=
−
+
+
+
−
40.
61x815x1x43x
=−−++−++
41. 4
41x2x
++=+
42.
1)x1(x2)x1(x2x1x
4
=−−−+−+
43.
x11x2x
24
−=+−
44.
1x(68x1x43x
−−++−−+
= 1 45. x
xx

x
2
3
xxxx
+
=−−+
46. x.
23x2
3x2
x3
=−−
−
47. x
2
+
55x
=+
48. x
2
+
11x
2
=+
49.
3
33
3x22x1x
−=−+−
50.
3x17x

4
4
=−+
51.
31x2x
3
=++−
52.
6x12x24
3
=−++
53.
3
32
23x1x
=−−−
54.
1x
2
1
x
2
1
3
=−++
55.
6
2
33
1x1x1x

−=−−+
56.
3)x6)(x3(x63x
=−+−−++
57.
13x34x
33
=−−+
58.
3
3
1x221x
−=+
59.
2x14x12
33
=++−
60.
3
3
3
1x216x1x2
+−=−
61.
22
x1xx1x
−=−+
62.
2323
x22x)x1(x

−=−+
63.
1xxx21
24
−=−−
64.
x3x93x93
22
−=−−−−+
65.
2xxxx
=−++
66.
1449x14x49x14x
=−−+−+
67.
275x232x5x22x
=−+++−+−
68.
9x6x69x6x
−−−=−+
69.
1x1x2x1x2x
−=−−+−+
70.
3
3
x1
x23
x23

x1
−
+
+
+
−
=2 71.
4
1x
1x
1x
1x
44
=
+
−
+
−
+
72.
25
x16
1x
1x
x16
5
5
=
−
+

−
73.
1
4
1
x
2
1
xx
=++++
73.
4x5x23x4x2x3x
222
+−=+−++−
74.
4x3x23x2x2xx
222
−−=−−+−−
75.
1x2x1x21
22
=+−+
76.
4 2
4
2
4
2
1x
2

3
)1x()1x( −=+−−
77.
x235x7x7xx
2
−=++++
78.
x2)1x1(2x)1x1(2x
=+−+++++
79.
02xx
2
=−−
80. 7
18x)2x(x
+=−
81.
3x6x22x
2
+−=−
82.
02x5x2
2
=−−
83.
x212x3x
2
−=+−
84
1x2x2x

22
−=−
85.
41x23x
=−+−
2.