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

Bài tập cơ bản phương trình vô tỷ dành cho các em học sinh lớp 9 tự giải ôn luyện chuyên đề thường xuất hiện trong các đề thi vào 10 này.

Bài 1: Giải các phương trình sau:
1. $sqrt{{{x}^{2}}-6x+9}=x$

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

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

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

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

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

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

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

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

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

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

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

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

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

23. $sqrt{{{x}^{2}}}=x$

24. $sqrt{{{x}^{2}}-2x+1}=x-1$

25.$sqrt{{{x}^{2}}-4x+4}=x-2$

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

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

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

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

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

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

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

33. $sqrt{{{x}^{2}}}=-x$

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

35. $sqrt{{{x}^{2}}-4x+4}=2-x$

36. $sqrt{{{x}^{2}}+4x+4}=-x-2$

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

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

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

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

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

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

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

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

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

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

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. $sqrt{x+2sqrt{x}+1}+sqrt{x-2sqrt{x}+1}=2$

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

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

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

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

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

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

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

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

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

Bài 2: Giải các phương trình sau:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

24. $sqrt{x-1}=2$

25. $sqrt{2x-3}=13$

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

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

28. $3sqrt{x}=-1$

29. $sqrt{x-1}+2=0$

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

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

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

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

43. $sqrt{{{x}^{2}}-x}=x$

44. $sqrt{{{x}^{2}}-1}=x-1$

45. $sqrt{3-{{x}^{2}}}=x$

46. $sqrt{{{x}^{2}}-2x+2}=x-1$

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

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

49. $sqrt{x}-x=0$

50. $sqrt{x}+x=0$

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. $sqrt{10left| x right|-10}-6x=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. $left| 1-2x right|=6-sqrt{2x-1}$

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. $sqrt{frac{6x-4}{x}}=frac{x}{3x-2}+1$

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

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

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

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

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

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

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

28. $frac{left( 5-x right)sqrt{5-x}+left( x-3 right)sqrt{x-3}}{sqrt{5-x}+sqrt{x-3}}=2$
Bài 4: Giải các phương trình sau:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Bài 5: Giải các phương trình sau:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Bài 6: Giải các phương trình sau:

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

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

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

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

Bài 7: Giải các bất phương trình sau:

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

2. $sqrt{5-x}le 2x-7$

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

4. $sqrt{{{x}^{2}}-x-12}<7-x$

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

6. $sqrt{{{x}^{2}}-3x-10}le x-2$

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

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

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

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

11. $sqrt{{{x}^{2}}+3x-3}le 2x-3$

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

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

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

15. $sqrt{x+3}<x+1$

16. $sqrt{2x+12}<x+2$

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

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

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. $sqrt{3x-5{{x}^{2}}}ge 5x-2$

2. $sqrt{5-x}ge 2x-7$

3. $sqrt{x+1}ge 2x-1$

4. $sqrt{{{x}^{2}}-x-12}ge 7-x$

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

6. $sqrt{{{x}^{2}}-3x-10}ge x-2$

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

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

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

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

11. $sqrt{{{x}^{2}}+3x-3}le 2x-3$

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

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

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

15. $sqrt{x+3}>x+1$

16. $sqrt{2x+12}>x+2$

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

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

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

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