Bài tập cơ bản giải phương trình vô tỷ – Toán 9

Bài tập giải phương trình vô tỷ mức độ cơ bản dành cho học sinh lớp 9.

Bài 1: Giải các phương trình sau:
1.

2. displaystylesqrt{4{{x}^{2}}-12x+9}=x-1

3. x+sqrt{4{{x}^{2}}-4x+1}=2

4. 1-sqrt{4{{x}^{4}}-20{{x}^{2}}+25}=0

5. {{x}^{2}}-sqrt{{{x}^{2}}}=0

6. {{x}^{2}}+sqrt{{{x}^{2}}}=0

7. x+sqrt{{{x}^{2}}-4x+4}=0

8. x-sqrt{4{{x}^{2}}-12x+9}=0

9. 3x-1-sqrt{4{{x}^{2}}-12x+9}=0

10. x-sqrt{4{{x}^{2}}-12x+9}=3

11. displaystylesqrt{3-2sqrt{2}}-sqrt{{{x}^{2}}+2xsqrt{3}+3}=0

12. displaystylesqrt{5{{x}^{2}}-2xsqrt{5}+1}=sqrt{6-2sqrt{5}}

13. displaystylesqrt{4{{x}^{2}}+4xsqrt{7}+7}-sqrt{8-2sqrt{7}}=0

14. displaystylesqrt{7-2sqrt{10}}-sqrt{5{{x}^{2}}-2xsqrt{10}+2}=0

15. displaystylesqrt{11+6sqrt{2}}=sqrt{2{{x}^{2}}-6xsqrt{2}+9}

16. displaystylesqrt{11-sqrt{120}}=sqrt{5{{x}^{2}}+xsqrt{120}+6}

17. displaystylesqrt{1+2xsqrt{3}+3{{x}^{2}}}-sqrt{3+2xsqrt{3}+{{x}^{2}}}=0

18. displaystylesqrt{5{{x}^{2}}-2xsqrt{5}+1}-sqrt{4{{x}^{2}}+4xsqrt{5}+5}=0

19. displaystylesqrt{16{{x}^{2}}+8xsqrt{2}+2}-sqrt{9{{x}^{2}}-6xsqrt{2}+2}=0

20. displaystylesqrt{2{{x}^{2}}-2xsqrt{6}+3}-sqrt{2-2xsqrt{6}+3{{x}^{2}}}=0

21. displaystylesqrt{8{{x}^{2}}-4xsqrt{2}+1}-sqrt{{{x}^{2}}-6xsqrt{2}+18}=0

22. displaystylesqrt{5{{x}^{2}}+2xsqrt{30}+6}-sqrt{6{{x}^{2}}+2xsqrt{30}+5}=0

23. displaystylesqrt{{{x}^{2}}}=x

24. displaystylesqrt{{{x}^{2}}-2x+1}=x-1

25. displaystylesqrt{{{x}^{2}}-4x+4}=x-2

26. displaystylesqrt{16-8x+{{x}^{2}}}=4-x

27. displaystylesqrt{4{{x}^{2}}-12x+9}=2x-3

28. displaystylesqrt{25{{x}^{2}}-10x+x}=5x-1

29. displaystylesqrt{{{x}^{2}}-2xsqrt{5}+5}=x-sqrt{5}

30. displaystylesqrt{3{{x}^{2}}-6xsqrt{2}+6}=sqrt{3}x-sqrt{6}

31. displaystylesqrt{10{{x}^{2}}-12xsqrt{10}+36}=sqrt{10}x-6

32. displaystylesqrt{7{{x}^{2}}+2xsqrt{14}+2}=sqrt{7}x+sqrt{2}

33. displaystylesqrt{{{x}^{2}}}=-x

34. displaystylesqrt{{{x}^{2}}-6x+9}=3-x

35. displaystylesqrt{{{x}^{2}}-4x+4}=2-x

36. displaystylesqrt{{{x}^{2}}+4x+4}=-x-2

37. displaystylesqrt{4{{x}^{2}}+4x+1}=-2x-1

38. displaystylesqrt{{{x}^{2}}+x+frac{1}{4}}=-x-frac{1}{2}

39. displaystylesqrt{x+2sqrt{x}+1}-sqrt{x-2sqrt{x}+1}=2

40. displaystylesqrt{x+4sqrt{x}+4}+sqrt{x-4sqrt{x}+4}=4

41. displaystylesqrt{x+6sqrt{x}+9}-6=sqrt{9-6sqrt{x}+x}

42. displaystylesqrt{4x+4sqrt{x}+1}=sqrt{1-4sqrt{x}+4x}+2

43. displaystylesqrt{x-2sqrt{x-1}}-sqrt{x+2sqrt{x-1}}=-2

44. displaystylesqrt{x-2sqrt{x-2}-1}-sqrt{x+2+4sqrt{x-2}+3}=0

45. -sqrt{x+3+4sqrt{x-1}}+sqrt{x+8-6sqrt{x-1}}=-5

46. displaystylesqrt{x+4sqrt{x-4}}-sqrt{x-4sqrt{x-4}}=4

47. -sqrt{2x+4+6sqrt{2x-5}}+sqrt{2x-4-2sqrt{2x-5}}=-4

48. 4+sqrt{2x+6-6sqrt{2x-3}}=sqrt{2x-2+2sqrt{2x-3}}

49. displaystylesqrt{x+2sqrt{x}+1}+sqrt{x-2sqrt{x}+1}=2

50. displaystylesqrt{x-2sqrt{x-1}}+sqrt{x+2sqrt{x-1}}=2

51. displaystylesqrt{x-2sqrt{x-2}-1}+sqrt{x+2+4sqrt{x-2}}-3=0

52. displaystylesqrt{x+3+4sqrt{x-1}}+sqrt{x+8-6sqrt{x-1}}=5

53. displaystylesqrt{x+4sqrt{x-4}}+sqrt{x-4sqrt{x-4}}=4

54. displaystylesqrt{2x+4+6sqrt{2x-5}}+sqrt{2x-4-2sqrt{2x-5}}=4

55. displaystylesqrt{2x+2sqrt{2x}+1}-sqrt{2x-2sqrt{2x}+1}=2

56. displaystylesqrt{4+4sqrt{3x}+3x}-4=sqrt{4-4sqrt{3x}+3x}

57. displaystylesqrt{12x-4sqrt{3}x+1}-sqrt{1+4sqrt{3}x+12x}=-2

58. displaystylesqrt{18x+6sqrt{2}x+1}-sqrt{1-6sqrt{2}x+18x}=2.

Bài 2: Giải các phương trình sau:

1. displaystylesqrt{2x-3}=sqrt{x-1}

2. displaystylesqrt{2x-3}-sqrt{x+3}=0

3. displaystylesqrt{x-1}=sqrt{2x+3}

4. displaystylesqrt{2x-3}=sqrt{x+1}

5. displaystylesqrt{x+2}=sqrt{2x-4}

6. displaystylesqrt{2-x}=sqrt{3+x}

7. displaystylesqrt{1-x}-sqrt{x-3}=0

8. displaystylesqrt{-2x}-sqrt{2-x}=0

9. displaystylesqrt{6-x}-sqrt{-3x}=0

10. displaystylesqrt{{{x}^{2}}-3x}-sqrt{5left( 3-x right)}=0

11. displaystylesqrt{x-2}=sqrt{x-2}

12. displaystyle sqrt{4x-8}=2sqrt{x-2}

13. displaystylesqrt{x-1}-sqrt{x-4}=0

14. displaystylesqrt{2-x}-sqrt{3-x}=0

15. displaystylesqrt{{{x}^{2}}-5}=sqrt{4x-9}

16. displaystylesqrt{2{{x}^{2}}-6x+2}=sqrt{{{x}^{2}}-3x}

17. displaystylesqrt{{{x}^{2}}-2x-4}=sqrt{2-x}

18. displaystylesqrt{{{x}^{2}}-x-1}=sqrt{x-1}

19. displaystylesqrt{x-2}-sqrt{{{x}^{2}}-2x}=0

20. displaystylesqrt{{{x}^{2}}-x-2}=sqrt{x+1}

21. displaystylesqrt{2{{x}^{2}}-10x+11}=sqrt{{{x}^{2}}-6x+8}

22. displaystylesqrt{2{{x}^{2}}+6x-3}=sqrt{{{x}^{2}}+4x}

23. displaystylesqrt{2{{x}^{2}}+x-9}=sqrt{{{x}^{2}}-x-6}

24. displaystylesqrt{x-1}=2

25. displaystylesqrt{2x-3}=13

26. displaystylesqrt{2x-3}=sqrt{2}

27. displaystylesqrt{xleft( x-2 right)}-sqrt{3}=0

28. 3sqrt{x}=-1

29. displaystylesqrt{x-1}+2=0

30. 6-sqrt{2x+3}=12

31. 3sqrt{{{x}^{2}}-x}-sqrt{54}=0

32. 2sqrt{2}-sqrt{{{x}^{2}}+2x}=0

33. 2sqrt{3}-sqrt{7x-{{x}^{2}}}=0

34. 3-sqrt{{{x}^{2}}+3}=0

35. 2-sqrt{xleft( 4-x right)}=0

36. 3-sqrt{-xleft( x+6 right)}=0

37. 2-sqrt{{{x}^{2}}-1}=0

38. 1-sqrt{{{x}^{2}}-2}=0

39. displaystylesqrt{16}-2sqrt{{{x}^{2}}+3x}=0

40. 2sqrt{3}-sqrt{xleft( x+7 right)}=0

41. displaystylesqrt{3-x}=3x-5( PTNK, CD, 1999-2000)

42. x-sqrt{4x-3}=2 ( PTNK, AB, 2004-2005, Vòng 1)

43. displaystylesqrt{{{x}^{2}}-x}=x

44. displaystylesqrt{{{x}^{2}}-1}=x-1

45. displaystylesqrt{3-{{x}^{2}}}=x

46. displaystylesqrt{{{x}^{2}}-2x+2}=x-1

47. displaystylesqrt{5-{{x}^{2}}}=x-1( LÊ HỒNG PHONG, 2006-2007, Vòng 1)

48. x-2=sqrt{{{x}^{2}}-4x+3}

49. displaystylesqrt{x}-x=0

50. displaystylesqrt{x}+x=0

51. x-sqrt{2x-9}=6

52. 2x-sqrt{4x-1}=0

53. 3x-sqrt{6x-1}=0

54. x-2sqrt{x-1}=16

55. x+sqrt{-left( 2x+1 right)}=0

56. x+2sqrt{x-1}=0

57. x+sqrt{3left( 6-x right)}=0

58. x+sqrt{x+3}=0

59. x+sqrt{2x+3}=0

60. x+sqrt{5-4x}=0

61. 2x+sqrt{3x+7}=0

62. 3x+sqrt{5x+4}=0

63. 2x-sqrt{xleft( 1-2x right)}=1

64. x+sqrt{1-{{x}^{2}}}=1

65. x+sqrt{4-{{x}^{2}}}=2

66. 2x+sqrt{4left| x right|-1}=0

67. x+2sqrt{left| x right|-1}=0

68. -5x+sqrt{2left| x right|+3}=0

69. 3sqrt{-2left| x right|+1}=9x

70. 7x+sqrt{left| x right|-4}=0

71. displaystylesqrt{10left| x right|-10}-6x=0

72. displaystylesqrt{-3left| x right|+2}+1=x

73. displaystylesqrt{7left| x right|+11}+x+1=0

74. displaystylesqrt{2left| x-1 right|-3}-x+1=0

75. -3sqrt{2left| 2x+1 right|-5}+6x+3=0

76. 5sqrt{2left| 1-5x right|+3}-5+25x=0

77. -2sqrt{-8left| 2-3x right|+9}+4-6x=0

78. 7sqrt{-4left| 3x-9 right|+5}+21x-63=0

79. displaystylesqrt{-2left| 1-2x right|+3}+1=2x

80. displaystyle 3sqrt{2x}-5sqrt{8x}+7sqrt{18x}=8

81. displaystylefrac{5}{3}sqrt{15x}-sqrt{15x}+11=frac{1}{3}sqrt{15x}

82. displaystylesqrt{4x+20}-sqrt{x+5}-frac{1}{3}sqrt{9x+45}=4

83. displaystylesqrt{36x-36}-sqrt{9x-9}-sqrt{4x-4}=16-sqrt{x-1}

84. displaystylesqrt{36x-72}-sqrt{9x-18}+sqrt{4x-8}+sqrt{x-2}=sqrt{72}

85. displaystylesqrt{9x+18}-sqrt{x+2}-sqrt{4x+8}+2sqrt{x+5}=0

86. displaystylefrac{5}{3}sqrt{45x}-sqrt{125x}-frac{1}{3}sqrt{405x}-2sqrt{16-16x}=0

87. displaystylefrac{1}{5}sqrt{25x-125}-frac{3}{2}sqrt{x-5}+sqrt{36x-180}+sqrt{9x-27}=0

88. displaystylesqrt{36x-216}-sqrt{x-6}+frac{7}{2}sqrt{4x-24}=frac{3}{7}sqrt{49x-343}

89. 15sqrt{x-7}-2sqrt{9x-63}-9sqrt{25x-175}=sqrt{4x-24}

90. displaystyle sqrt{49x-98}-sqrt{9x-18}-sqrt{16x-32}=sqrt{4x-4}

91. 7sqrt{x}+sqrt{81x-81}+sqrt{x-1}=sqrt{100x-100}

92. displaystylesqrt{{{x}^{2}}-2xsqrt{5}+5}+sqrt{{{x}^{2}}-xsqrt{5}}=0

93. displaystylesqrt{0,2{{x}^{2}}-2x+5}+sqrt{3{{x}^{2}}-15x}=0

94. displaystylesqrt{{{x}^{2}}+4x}+sqrt{frac{{{x}^{2}}}{2}-8}=0

95. displaystylesqrt{x-1}+sqrt{{{x}^{2}}-3x+2}=0

96. displaystylesqrt{2+x}+sqrt{4{{x}^{2}}-6x-10}=0

97. displaystylesqrt{{{x}^{2}}-9}+sqrt{{{x}^{2}}-4x+3}=0

98. displaystylesqrt{-2{{x}^{2}}+3x+5}+sqrt{2{{x}^{2}}-7x-15}=0

LUYỆN TẬP
Bài 3: Giải các phương trình sau:

1. {{x}^{2}}+4left( left| x-2 right|-x right)-1=0
a) Đặt t=left| x-2 right| để đưa phương trình trên về phương trình theo ẩn t.
b) Tìm t rồi sau đó tìm x.

2. {{x}^{2}}+2left( left| x-1 right|-x right)-2=0

3. {{x}^{2}}+3left( left| x-3 right|-2x right)-9=0

4. {{x}^{2}}+4left( left| x-4 right|-2x right)+4=0

5. {{x}^{2}}+left( x+left| x+1 right| right)-14=0 (PTNK BAN CD 2006-2007)

6. 7-4sqrt{2x-1}=3left| 1-2x right|

a) Đặt t=sqrt{3-2x} để đưa phương trình trên về phương trình theo ẩn t.

b) Tìm t rồi sau đó tìm x.

7. 5-sqrt{3-2x}=left| 2x-3 right| (PTNK BAN CD 2000-2001)

8. 20-sqrt{3-2x}=left| 2x-3 right| (PTNK BAN CD 2004-2005)

9. 12-sqrt{4-3x}=left| 3x-4 right| (PTNK BAN CD 2007-2008)

10. displaystyleleft| 1-2x right|=6-sqrt{2x-1}

11. 2left| 4-3x right|+3sqrt{3x-4}-2=0

12. 3left| 3x-1 right|+8sqrt{1-3x}=3

13. 2sqrt{frac{6x-1}{2x}}=frac{2x}{6x-1}+1

a) Đặt t=sqrt{frac{6x-1}{2x}} để đưa phương trình trên về phương trình theo ẩn t.

b) Tìm t rồi sau đó tìm x.

14. 2sqrt{frac{3x-1}{x}}=frac{x}{3x-1}+1 (PTNK BAN CD 2001-2002)

15. 2sqrt{frac{6x-1}{2x}}=frac{2x}{6x-1}+1

16. 2sqrt{frac{9x-1}{3x}}=frac{3x}{9x-1}+1

17. 2sqrt{frac{3x-3}{x}}=frac{3x}{x-1}+1

18. displaystylesqrt{frac{6x-4}{x}}=frac{x}{3x-2}+1

19. displaystylesqrt{frac{2x-1}{x}}+1+sqrt{frac{x}{2x-1}}=3frac{x}{2x-1}

20. 2sqrt{frac{x}{x-1}}-sqrt{frac{x-1}{x}}=2frac{x-1}{x}+3

21. 3sqrt{frac{2x}{x-1}}+4sqrt{frac{x-1}{2x}}=3frac{x-1}{2x}+10

22. displaystylesqrt{frac{x}{3-2x}}+5sqrt{frac{3-2x}{x}}=4frac{3-2x}{x}+5

23. 2sqrt{frac{2x+1}{x}}-3sqrt{frac{x}{2x+1}}=4frac{x}{2x+1}+7

24. displaystylefrac{2+sqrt{19-2x}}{x}=1

25. displaystylesqrt{x}-frac{4}{sqrt{2+x}}+sqrt{2+x}=0

26. displaystylesqrt{9-5x}=sqrt{3-x}+frac{6}{sqrt{3-x}}

27. displaystylesqrt{2-x}+frac{4}{3+sqrt{2-x}}=2

28. displaystylefrac{left( 5-x right)sqrt{5-x}+left( x-3 right)sqrt{x-3}}{sqrt{5-x}+sqrt{x-3}}=2

Bài 4: Giải các phương trình sau:

1. displaystylesqrt{2x+3}+sqrt{2x+2}=1

2. displaystylesqrt{1-x}+sqrt{4+x}=3

3. displaystylesqrt{x+4}-sqrt{2x-6}=1 ( PTNK, AB, 2006-2007, Vòng 1)

4. displaystylesqrt{3x-5}+sqrt{2x+3}=sqrt{x+2} (HSG, Q. Tân Bình, 2003-2004)

5. displaystylesqrt{x-2}+sqrt{x-1}=sqrt{2x-3} ( LÊ HỒNG PHONG 2001-2002, Vòng 1)

6. displaystylesqrt{3x+7}-sqrt{x+1}=2

7. displaystylesqrt{x+3}+sqrt{x-1}=2

8. displaystylesqrt{x+5}+sqrt{3-x}=4

9. displaystylesqrt{{{x}^{2}}+9}-sqrt{{{x}^{2}}+7}=2

10. displaystylesqrt{2-{{x}^{2}}}+sqrt{{{x}^{2}}+8}=4

11. displaystylesqrt{x+3}-sqrt{7-x}=sqrt{2x-8}

12. displaystylesqrt{2-x}=sqrt{7-x}-sqrt{-3-2x}

13. displaystylesqrt{11-x}-sqrt{x-1}=2

14. displaystylesqrt{{{x}^{2}}+3x+2}-sqrt{{{x}^{2}}+x+1}=1

15. displaystylesqrt{5x-1}=sqrt{3x-2}-sqrt{2x-3}

16. displaystylesqrt{5x-1}-sqrt{x-1}=sqrt{2x-4}

17. displaystylesqrt{x+2}-sqrt{2x-3}=sqrt{3x-5} (HSG, Q.I,1999-2000)

18. displaystylesqrt{x+4}-sqrt{1-x}=sqrt{1-2x}

19. displaystylesqrt{x+9}=5-sqrt{2x+4}

20. displaystylesqrt{3x+4}-sqrt{2x+1}=sqrt{x+3}

21. displaystylesqrt{x+12}+sqrt{x-6}-sqrt{x+2}-sqrt{x-4}=0

22. displaystylesqrt{3x+6}+sqrt{3x-3}-sqrt{3x+1}-sqrt{3x-2}=0

23. displaystylesqrt{x+4}+sqrt{x-5}-sqrt{x-1}-sqrt{x-4}=0

24. displaystylesqrt{2x+6}+sqrt{2x-3}-sqrt{2x+1}-sqrt{2x-2}=0

25. displaystylesqrt{x+6}+sqrt{x-3}-sqrt{x+1}-sqrt{x-2}=0 (PTNK, AB, 2005-2006, Vòng 1)

26. displaystyleleft{ begin{array}{l}x-y=5\sqrt{2x+1}-sqrt{y+2}=2end{array} right. ( PTNK, AB, 2005-2006, Vòng 1)

27. displaystylesqrt{x+sqrt{x+11}}+sqrt{x-sqrt{x+11}}=4

28. displaystylesqrt{x-sqrt{x-2}}+sqrt{x+sqrt{x-2}}=3

29. displaystylefrac{2-sqrt{x}}{2-x}=sqrt{frac{2}{2-x}}

30. displaystylesqrt{frac{20+x}{x}}+sqrt{frac{20-x}{x}}=sqrt{6} ( đặt t=frac{20}{x})

Bài 5: Giải các phương trình sau:

1. displaystylesqrt{2x+1}+sqrt{x-3}=2sqrt{x}

2. displaystylesqrt{x+2}-sqrt{2x-3}=sqrt{4x-7}

3. displaystylesqrt{x}+sqrt{x-3}=sqrt{3left( x-1 right)}

4. displaystylesqrt{x-2}+sqrt{4-x}=sqrt{6-x}

5. displaystylesqrt{x+5}=2sqrt{x}-sqrt{2x-7}

6. displaystylesqrt{3x+12}-sqrt{4x+13}=sqrt{x+1}

7. displaystylesqrt{9-x}-sqrt{x+4}=sqrt{3x+1}

8. displaystylesqrt{3x+4}=2sqrt{x}-sqrt{x-4}

9. displaystylesqrt{2x+5}=sqrt{12x+25}-sqrt{5x+6}

10. displaystylesqrt{x+1}+sqrt{x-1}=sqrt{3x-1}

11. displaystylesqrt{3x-5}+sqrt{2x-3}=sqrt{x+2}

12. displaystylesqrt{{{x}^{2}}+9}-sqrt{{{x}^{2}}-7}=2

13. displaystylesqrt{{{x}^{2}}+5}+sqrt{{{x}^{2}}-3}=4

14. displaystylesqrt{{{x}^{2}}-3x+6}+sqrt{{{x}^{2}}-3x+3}=3

15. displaystylesqrt{3{{x}^{2}}-2x+15}+sqrt{3{{x}^{2}}-2x+8}=7

16. displaystylesqrt{3{{x}^{2}}+5x+8}-sqrt{3{{x}^{2}}+5x+1}=1

Bài 6: Giải các phương trình sau:

1. displaystylesqrt{x+6}+sqrt{x-3}-sqrt{x+1}-sqrt{x-2}=0

2. displaystylesqrt{{{x}^{2}}+x-5}+sqrt{{{x}^{2}}+8x-4}=5

3. displaystylesqrt{3{{x}^{2}}+6x+16}+sqrt{{{x}^{2}}+2x}=2sqrt{{{x}^{2}}+2x+4}

4. displaystylesqrt{2{{x}^{2}}-9x+4}+3sqrt{2x-1}=sqrt{2{{x}^{2}}+21x-11}

Bài 7: Giải các bất phương trình sau:

1. displaystylesqrt{3x-5{{x}^{2}}}le 5x-2 (PTNK, AB, 2006-2007, Vòng 1)

2. displaystylesqrt{5-x}le 2x-7

3. displaystylesqrt{x+1}<2x-1 (PTNK, AB, 2002-2003, Vòng 1)

4. displaystylesqrt{{{x}^{2}}-x-12}<7-x

5. 1-x+sqrt{2{{x}^{2}}-3x-5}<0

6. displaystylesqrt{{{x}^{2}}-3x-10}le x-2

7. 3sqrt{-{{x}^{2}}+x+6}+2left( 2x-1 right)<0

8. displaystylesqrt{3{{x}^{2}}+13x+4}+2-xle 0

9. 2sqrt{3x+{{x}^{2}}}le 2x-1

10. displaystylesqrt{{{x}^{2}}-3x+3}le 2x-1

11. displaystylesqrt{{{x}^{2}}+3x-3}le 2x-3

12. -6x+7ge sqrt{{{x}^{2}}-6x+7}

13. displaystylesqrt{{{x}^{2}}-3x-10}le 8-x

14. displaystylesqrt{{{x}^{2}}+5x-6}<2x+3

15. displaystylesqrt{x+3}<x+1

16. displaystylesqrt{2x+12}<x+2

17. displaystyle sqrt{{{x}^{2}}-6x-40}le 16-x

18. displaystylesqrt{{{x}^{2}}+10x+4}le 2x-4

19. 3sqrt{-{{x}^{2}}+3x+54}+4x-6<0

20. 2-x+sqrt{2{{x}^{2}}-6x-20}<0

Bài 8: Giải các bất phương trình sau:

1. displaystylesqrt{3x-5{{x}^{2}}}ge 5x-2

2. displaystylesqrt{5-x}ge 2x-7

3. displaystylesqrt{x+1}ge 2x-1

4. displaystylesqrt{{{x}^{2}}-x-12}ge 7-x

5. 1-x+sqrt{2{{x}^{2}}-3x-5}>0

6. displaystylesqrt{{{x}^{2}}-3x-10}ge x-2

7. 3sqrt{-{{x}^{2}}+x+6}+2left( 2x-1 right)>0

8. displaystylesqrt{3{{x}^{2}}+13x+4}+2-xge 0

9. 2sqrt{3x+{{x}^{2}}}ge 2x-1

10. displaystylesqrt{{{x}^{2}}-3x+3}ge 2x-1

11. displaystylesqrt{{{x}^{2}}+3x-3}le 2x-3

12. -4x+2le 4sqrt{{{x}^{2}}-6x+5}

13. displaystylesqrt{{{x}^{2}}-3x-10}ge 8-x

14. displaystylesqrt{{{x}^{2}}+5x-6}>2x+3

15. displaystylesqrt{x+3}>x+1

16. displaystylesqrt{2x+12}>x+2

17. displaystyle sqrt{{{x}^{2}}-6x-40}ge 16-x

18. displaystylesqrt{{{x}^{2}}+10x+4}ge 2x-4

19. 3sqrt{-{{x}^{2}}+3x+54}+4x-6>0

20. 2-x+sqrt{2{{x}^{2}}-6x-20}>0

Đại số 9 – Tags: phương trình vô tỷ, toán 9

  • Ví dụ tìm điều kiện xác định của biểu thức chứa căn

  • Một số ví dụ vẽ đồ thị hàm số bậc nhất y=ax+b

  • Khảo sát và vẽ đồ thị hàm số bậc hai y=ax^2

  • Cách vẽ đồ thị hàm số bậc nhất y=ax+b

  • 5 bài tập giải hệ PT bằng phương pháp cộng đại số có lời giải

  • Giải hệ phương trình bằng phương pháp thế

  • Giải bài toán bằng cách lập hệ phương trình