BÀI TẬP PT - BPT VÔ TỶ

B I T À Ậ P

PHƯƠNG TRÌNH VÔ TỶ BẤT PHƯƠNG TRÌNH VÔ TỶ

2

1 2 2 3 1; 2;

2

x− + x− = x− x= x= x= 

3 2 8 3 2 15 7 ; 1

3

x − x+ + x − x+ = x= − x= 

4) x+ −8 2 x+ = −7 2 x+ −1 x+7 (x=2)

5) 4 x− x2 − + 1 x+ x2 − = 1 2 (x= 1)

1 2 2 1 1;

2

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

2 x 2 x x 2 x 2

9) 1 1 3 2 ( 1)

3 2

x x

x

−

10) x− + 4 x2 − − = 3x 4 x x( = 8)

11) 3 6x+ = 1 8x3 − 4x− 1

2

x

x+ x− + x− x− = + x= x=

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

3

x

x + + + = − + + +

15) 3 x+ + 1 3 x+ = + 2 1 3 x2 + 3x+ 2(x = 0; x = - 1)

3

x

x

+ + =

+ (x = 1)

17)3(2+ x−2) 2= x+ x+6

2 1 ( 1)

x− x− − −x x+ x −x

19) 2x2+8x+ +6 x2− =1 2x+2

20)(x+ 3 10) −x2 =x2 − −x 12

21) x− x2 − + 1 x+ x2 − = 1 2

2

1 2

1 1

2

3

x

x

23) x+ 5+ x− =1 6

24) x+ 4−x2 = +2 3x 4−x2

26) (4x−1) x2+ =1 2x2+2x+1

2(1 −x x) + 2x− = 1 x − 2x− 1 28) x2 + 2x+ 2x− = 1 3x2 + 4x+ 1

29) x2 + −(3 x2 + 2)x= + 1 2 x2 + 2

30) 4 x+ − = 1 1 3x+ 2 1 − +x 1 −x2 31) x2 +3x+ = +1 (x 3) x2 +1 32) x3 + = 2 3 3 3 x− 2

33) 1 + 1 −x2 =x(1 2 1 + −x2)

………

1) (x2 +x-2) 2x2 −1<0

2) 3(4 2 9) 2 3

2

3 3

x

x x

− 3) x2 + + +3x 2 x2 + + ≤6x 5 2x2 + +9x 7 4) x2 + − +x 2 x2 + − ≤2x 3 x2 + −4x 5 5) 2x2 + + +8x 6 x2 − ≤ +1 2x 2 6) 5x2 +10 1 7x+ ≥ − −x2 2x

7) 2x 2 +4x+3 3 2x x− − 2>1 9) 4 2 2 1 2

2

x x

x x

+ < + +

10) x x( −4) − + + −x2 4x (x 2)2 <2 11)

2

51 2x x

1

1 x

−

1) 12)

2

2 x

13) 2 x 4x 3

2 x

− + − ≥

14)

2 2

x

x 4

15)Xđ m để bpt: m x( 2 − 2x+ + + 2 1) x(2 −x) ≤ 0, (1)

có nghiệmx∈0;1+ 3 .

16)Xđ m để bpt sau có nghiệm: mx− x− ≤ + 3 m 1

17)Tìm m để phương trình sau có nghiệm:

2

25) 2 1

x

+ − = +