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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. $\sqrt{x^2-3x}-\sqrt{5(3-x)}=0$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

35. $2-\sqrt{x(4-x)}=0$

36. $3-\sqrt{-x(x+6)}=0$

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

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

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

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

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. $x-2\sqrt{x-1}=16$

55. $x+\sqrt{-(2x+1)}=0$

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

57. $x+\sqrt{3(6-x)}=0$

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. $2x-\sqrt{x(1-2x)}=1$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

LUYỆN TẬP
Bài 3: Giải các phương trình sau:

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

2. $x^2+2(|x-1|-x)-2=0$

3. $x^2+3(|x-3|-2x)-9=0$

4. $x^2+4(|x-4|-2x)+4=0$

5. $x^2+(x+|x+1|)-14=0$ (PTNK BAN CD 2006-2007)

6. $7-4\sqrt{2x-1}=3|1-2x|$
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. $5-\sqrt{3-2x}=|2x-3|$ (PTNK BAN CD 2000-2001)

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

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

10. $|1-2x|=6-\sqrt{2x-1}$

11. $2|4-3x|+3\sqrt{3x-4}-2=0$

12. $3|3x-1|+8\sqrt{1-3x}=3$

13. $2\sqrt{\frac{6x-1}{2x}}=\frac{2x}{6x-1}+1$
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. $2\sqrt{\frac{3x-1}{x}}=\frac{x}{3x-1}+1$ (PTNK BAN CD 2001-2002)

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

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

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

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

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

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

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

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

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

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. $\frac{(5-x)\sqrt{5-x}+(x-3)\sqrt{x-3}}{\sqrt{5-x}+\sqrt{x-3}}=2$
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. $\{\begin{array}{l}x-y=5\\ \sqrt{2x+1}-\sqrt{y+2}=2\end{array}$ ( 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. $\sqrt{2x+1}+\sqrt{x-3}=2\sqrt{x}$

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

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

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

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

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

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

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

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

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

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

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

Bài 7: Giải các bất phương trình sau:

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

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

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

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

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

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

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

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

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

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

Bài 8: Giải các bất phương trình sau:

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

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

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

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

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

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

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

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

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

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

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

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

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

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