Bai tap 21 PTHPT On thi Dai hoc

BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ 1.[r]

BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ

1. x2

+√x2− 6=12 (VH-98)

2. x2

+√x2

5. √3 x2−9 x+ 1+ x −2=0

6. √x2−2 x − 8=√3(x − 4) (BD-01)

7. (x − 3)√x2− 4=x2− 9 (Y HCM-01)

8. √x2−6 x +6=2 x −1 (XD-01)

9. √x2

10. √x2−3 x+2=2 x −1

12. √x+3+1=√3 x −1

13. √x −5+√x +3=√2 x+4 (HH-98)

14. √3 x +4 −√2 x −1=√x +3 (NH-98)

15. √x2−3 x+ 3+√x2−3 x +6=3 (TM-98)

16. √x+2 −√2 x −3=√3 x −5 (BK-94)

17. √3 x −3 −√5 − x=√2 x − 4 (A05)

18. √x2+8=2009 x −2008+√x2+3

19. 2√x +2+2√x +1 −√x+1=4 (D05)

20. √x+1 −1=√x −√x+8

21. 3

√x −1+√3 x − 2=√3 2 x −3 (Đề 113)

22. 3

√x+34 −3

√x −3=1 (Đề 12)

23. 3

√x+1+√3 x − 1=√35 x

24. x√3 16 −√3 2 x+1=√32 x − 1

25. √x(x −1)+√x (x +2)=2√x2 (SP2-A00)

26. √x −1

x −√1−1

x=

x −1 x

27. √2 x2+8 x+6+√x2−1=2 x +2

28. x − 2√x − 1−(x − 1)√x+√x2− x=0

29. √x+3+ 2 x√x +1=2 x+√x2+4 x+3

30. √x+1 −√x+ 2+√x +2

x +1=1

31. (1+x√x2+1)( √x2+1 − x)=1

32. (x+5)(2− x )=3√x2+3 x

33. x√x+ 1+√x2− x+ 1=x +√x3+1

34. √x2−3 x+2+√x +3=√x −2+√x2+2 x −3

35. √2 x2

+x+√2 x2+2 x=√x2

+2 x +√x2+3 x

36. √(x − 1)(2 x +7)+√3(x − 1)(x −6)=√(x −1)(7 x +1)

37. √x3+x2+3 x+3+√2 x=√x2+3+√2 x2+2 x

38. x√x2+x +1+√x2− x +1=x +√x4+x2+1

39. √x2−3 x+2+√x +3=√x −2+√x2+2 x −3

40. x√1+1

x+

1

x√x +2−√x +2

x+3=1

41. √x+3+2 x√2 x+1=2 x+√2 x2+7 x +3

42. √x +3

x +2 x√2 x − 1−√2 x2

√x +3+x√x +8=2 x

2

+x +2√x+8

x +3

44. 3

√x+1+√3 x2

=√3 x+√3x2

+x

45. 4

√x+1+√x −√4x3+x2=1

46. 2+ x

√2+√2+x+

2 − x

√2−√2+x=2√2

2

√3 x − 2 −√3 x − 2=1 − x (Đề 124)

48. √3 2 x

x +1+

3

√1

2+

1

2 x=2 (GT-95)

49. x2+2 x +4=3√x3

+4 x

50. √x2+91=√x −2+x2

51. x212 5 3  x x25

52. 3(2+√x − 2)=2 x +√x+6 (KTQS-01)

53. √5

4− x

2

+√1 − x2+√5

4− x

2

−√1− x2=x+1

54. √x+2√x −1 −√x − 2√x − 1=2 (BCVT-00)

55. √x+2√x −1+√x − 2√x −1= x+3

2 (TCKT-95)

56. √4 x −√x2− 1+√x +√x2−1=2

57. x2

− x −√x2− x +13=7

58. x2

+2√x2−3 x +1=3 x +4

59. 2 x2+3√2 x2

+x+1=9 − x

60. x2

−√x2− 2 x +4=2 x − 2

61. 2 x2

+5√x2+3 x+ 5=23 − 6 x

62. √2 x2+5 x+2+√2 x2+5 x − 9=1

63. x2 4x8 x2 4x4  2x2 8x12

64. √x2−3 x+ 3+√x2−3 x +6=3 (TM-98)

65. √3− x+x2−√2+x − x2=1 (NT-99)

66. (x − 2)√x −1 −√2 x+2=0 (*)

67. √x+√x2− 1=9√2

4 (x − 1)√x −1 (*)

95. √2 x2+x+9+√2 x2− x+1=x+4

96. √2 x2+x+6+√x2+x +2=x +4

x

97. √2 x2+5 x+12+√2 x2+3 x +2=x +5

98. x2

+√x2+1=x +√x +1

99. 1+√x2+1=x +√x2+x

100. x+√3x3

+x+1=1+√3 x3

+2

68. √x+√9 − x=√− x2+9 x +9 (*)

69. √1+√1 − x2=x (1+2√1 − x2)

70. √x+2+√6 − x +√(x +2)(6 − x )=8

71. √1− x +√1+x+2√1 − x2=4

73. √x+1+√4 − x +√(x +1)(4 − x )=5 (NN-01)

74. x+√4 − x2=2+3 x√4 − x2 (MĐC-01)

75. √x+√x +1−√x2+x=1 (ĐHHP-00)

77. √ x

x − 1+√x −1

x =

3

√2 (ĐHTL-01)

78. √x −2 −√x +2=2√x2− 4 −2 x+2 (CĐSP-01)

79. 2 x +1+√x+3−√x =2√x2+3 x

80. 2 x2

+x +√x2+3+2 x√x2+3=9

81. √x+2+√2 x+5=3 x+ 2√2 x2+9 x +10+7

82. 1+√x +4+√3 x+1=4 x+2√(x +4 )(3 x+1)

83. √3 x −2+√x − 1=4 x − 9+2√3 x2−5 x +2 (QS97

)

84. x2+2 x +√x +3+2 x√x +3=9

85. x2

+4 x +1− 2 x√3 x +1=√3 x+1

86. 2 x +6+2√x2+3 x=4 (√x +√x+3)

87. 2√2 x − x2+4=3(√x+√2 − x )

88. 1+4 x2+(4 x −3)√x − 1=5 x

89. x2+x +6+2 x√x +3=4 (x+√x +3)

90. 2 x +√x+1+√x +2√x2+x=1

91. √2 x2+x+9+√2 x2− x+1=x+4

92. √x2

+x +1+√x2− x +1=2

93. √x2

+x +1=√x2− x +1+2 x

94. √x+3 −√1 − x=x +1

101. √2 x2

+x+1+√x2− x+1=3 x

102.

x+1¿2

¿

¿

3

√¿

103.

x+5¿2

¿

4 − x¿2

¿

¿

¿

3

√¿

104.

3 x +1¿2

¿

3 x −1¿2

¿

¿

¿

3

√¿

105.

x +6¿2

¿

3 − x¿2

¿

¿

¿

3

√¿

106. 4

√x+4

√x +1=4

√2 x +1

107. 2−√x¿

2

√2− x2

=¿

108. x2

− x −1000√1+8000 x=1000

109. 2 x3=1+√3 x+1

2

110. x3+2=33

√3 x −2

111. x3+1=2√32 x − 1

112. 3

√3 x −5=8 x3−36 x2+53 x −25

113. 8 x2

+8 x −5=√2 x+15

16

114. 7 x2+7 x=√4 x +9

28

115. x2

+√x +1=1 (XD-98)

116. x+√5+√x −1=6

117. 2 x =√1+3

2√1+3 x (*)

2√3+1

2√3+1

119. x2

− 4 x − 3=√x +5

120. √3 x +1=− 4 x2

+13 x − 5

√7+3

√x +78

123. 2√3x −2+5√x +1=12

124. 3

√x+7 −√x=1 (L-96)

125. 3

126. 4

√17− x2−√32 x2−1=1

127. 3

√x −2+√x +1=3

130. 7√x3−1=2 x2

+5 x −1

131. √x3+8

x2+8 =

1 3

132. x2 2x 2x 1 3x24x1

133. 5x2 14x 9 x2 x 20 5 x1

134. 8 x2

−3√8 x3+1+3=2 x

135. 2 x3+(x −2)√2 x3+5 x2+5 x+3=4 x2+x −2

136. 2 x2

+x +3=3 x√x +3

137. √x+8= 3 x

2

+7 x +8

4 x +2

139. 2(1 − x)√x2+2 x −1=x2−2 x − 1

141. x +2+x√2 x+1

x +√2 x +1 =√x +2

142. (√x+3 −√x +1)(x2

+√x2

+4 x +3)=2 x (*)

143. 4 x2

+3 x+3=4 x√x +3+2√2 x − 1

144. 4√x +3 −√x − 1=x+7

145. 2 x√x2− x +1+4√3 x +1=2 x2+2 x+6

148. 8 x2+3 x +7=6 x√x+8

149. 2 x√x+4=3 x2

+3 x − 3

150. (x+3)√x+3+3√x +3=8 x3+12 x2+3 x − 9

−6=0

152. √2 x −3+√5 −2 x=3 x2−12 x+14

153. √x −2+√4 − x=2 x2−5 x −1

154. √314 − x3

+x=2(1+√x2−2 x − 1)

155. √x+√x +1+√x2+x=1

157. 2√1 − x +√x=√2− x

158. 2 x +√2 − x2

+√42 − x4=4

159. √x2−2 x+5+√x −1=2 (NN-99)

161. 2+√x

3+√1 − x=√x+√1 − x

163. √x+4 −√2 x+3=x − 1

164. (x − 1)√x +1+√2 x +1=√x +2

165. 1

x2+√x +5=

1

x+√2 x+4

167. 4

√x+8+√x +4=√2 x+3+√3 x

168. 5

√x+3+√32 x+4=√52 x +2+√33 x+3

169 3

√3 x2− x+2009−√33 x2−7 x+2010+√36 x +2009=√32010