Bai tap 21 PTHPT On thi Dai hoc

BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ 1.[r]

BÀI TẬP PHƯƠNG TRÌNH VƠ TỶ 1. x2+√x2−6=12 (VH-98)

2. x2

+√x2+11=31

3. √16x+17=8x −23 (QG-D-97) 4. √51−2x − x2=1− x (TCKT-97) 5. √3x2−9x+1+x −2=0

6. √x2−2x −8

=√3(x −4) (BD-01) 7. (x −3)√x2−4=x2−9 (Y HCM-01) 8. √x2−6x

+6=2x −1 (XD-01) 9. √x2

+4x+x=1 (HVCTQG HCM-00) 10. √x2−3x+2=2x −1

11. √4−3√10−3x=x −2 (HSGQG-01) 12. √x+3+1=√3x −1

13. √x −5+√x+3=√2x+4 (HH-98) 14. √3x+4−√2x −1=√x+3 (NH-98) 15. √x2−3x+3+√x2−3x+6=3 (TM-98) 16. √x+2−√2x −3=√3x −5 (BK-94) 17. √3x −3−√5− x=√2x −4 (A05) 18. √x2+8=2009x −2008+√x2+3 19. 2√x+2+2√x+1−√x+1=4 (D05) 20. √x+1−1=√x −√x+8

21.

√x −1+√3 x −2=√3 2x −3 (Đề 113) 22.

√x+34−3

√x −3=1 (Đề 12) 23.

√x+1+√3 x −1=√35x 24. x√3 16−√3 2x+1=√32x −1

25. √x(x −1)+√x(x+2)=2√x2 (SP2-A00) 26. √x −1

x−√1−

1

x= x −1

x

27. √2x2+8x+6+√x2−1=2x+2 28. x −2√x −1−(x −1)√x+√x2− x=0

29. √x+3+2x√x+1=2x+√x2+4x+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+3x 33. x√x+1+√x2− x+1=x+√x3+1

34. √x2−3x+2+√x+3=√x −2+√x2+2x −3 35. √2x2

+x+√2x2+2x=√x2+2x+√x2+3x

36. √(x −1)(2x+7)+√3(x −1)(x −6)=√(x −1)(7x+1) 37. √x3+x2+3x+3+√2x=√x2+3+√2x2+2x

38. x√x2+x+1+√x2− x+1=x+√x4+x2+1 39. √x2−3x+2+√x+3=√x −2+√x2+2x −3 40. x√1+1

x+

1

x√x+2−√x+

2

x+3=1 41. √x+3+2x√2x+1=2x+√2x2+7x+3 42. √x+3

x +2x√2x −1−√2x

+5x −3=2 43. 4x+2

√x+3+x√x+8=2x

+x+2√x+8 x+3 44.

√x+1+√3 x2=√3 x+√3x2 +x 45.

√x+1+√x −√4x3+x2=1 46. 2+x

√2+√2+x+

2− x

√2−√2+x=2√2 47. x

2

√3x −2−√3x −2=1− x (Đề 124)

48. √3 2x x+1+

3 √1

2+

2x=2 (GT-95) 49. x2

+2x+4=3√x3+4x 50. √x2

+91=√x −2+x2

51. x212 3  x x25

52. 3(2+√x −2)=2x+√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√x2−3x+1=3x+4 59. 2x2

+3√2x2+x+1=9− x 60. x2−√x2−2x+4=2x −2 61. 2x2+5√x2+3x+5=23−6x 62. √2x2+5x+2+√2x2+5x −9=1

63. x2 4x8 x2 4x4  2x2 8x12 64. √x2−3x+3

+√x2−3x+6=3 (TM-98) 65. √3− x+x2−

√2+x − x2=1 (NT-99) 66. (x −2)√x −1−√2x+2=0 (*) 67. √x+√x2−1=9√2

4 (x −1)√x −1 (*)

95. √2x2+x+9+√2x2− x+1=x+4 96. √2x2+x+6+√x2+x+2=x+4

x 97. √2x2+5x+12+√2x2+3x+2=x+5 98. x2+√x2+1=x+√x+1

99. 1+√x2+1=x+√x2+x 100. x+√3x3

68. √x+√9− x=√− x2

+9x+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

72. √x+2+√5− x+√(x+2)(5− x)=4 (CĐBK-06) 73. √x+1+√4− x+√(x+1)(4− x)=5 (NN-01) 74. x+√4− x2=2+3x√4− x2 (MĐC-01) 75. √x+√x+1−√x2+x=1 (ĐHHP-00)

76. √3− x+√x −1−4√4x − x2−3=−2 (ĐHHP-01) 77. √ x

x −1+√

x −1

x =

3

√2 (ĐHTL-01)

78. √x −2−√x+2=2√x2−4−2x+2 (CĐSP-01) 79. 2x+1+√x+3−√x=2√x2+3x

80. 2x2+x+√x2+3+2x√x2+3=9

81. √x+2+√2x+5=3x+2√2x2+9x+10+7 82. 1+√x+4+√3x+1=4x+2√(x+4)(3x+1)

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

84. x2

+2x+√x+3+2x√x+3=9 85. x2+4x+1−2x√3x+1=√3x+1 86. 2x+6+2√x2+3x=4(√x+√x+3) 87. 2√2x − x2+4=3(√x+√2− x) 88. 1+4x2+(4x −3)√x −1=5x 89. x2+x+6+2x√x+3=4(x+√x+3) 90. 2x+√x+1+√x+2√x2+x=1 91. √2x2+x+9+√2x2− x+1=x+4 92. √x2

+x+1+√x2− x+1=2 93. √x2

+x+1=√x2− x+1+2x 94. √x+3−√1− x=x+1

101. √2x2

+x+1+√x2− x+1=3x 102.

x+1¿2 ¿ ¿

√¿

103.

x+5¿2 ¿

4− x¿2 ¿ ¿ ¿

√¿

104.

3x+1¿2 ¿

3x −1¿2 ¿ ¿ ¿

√¿

105.

x+6¿2 ¿

3− x¿2 ¿ ¿ ¿

√¿ 106.

√x+4

√x+1=√42x+1 107. 2−√x¿

2

√2− x2 =¿

108. x2− x −1000√1+8000x=1000 109. 2x3=1+√3 x+1

2

110. x3

+2=3√33x −2

111. x3+1=2√32x −1

112.

√3x −5=8x3−36x2+53x −25 113. 8x2

+8x −5=√2x+15

16

114. 7x2+7x=√4x+9

28

115. x2

+√x+1=1 (XD-98) 116. x+√5+√x −1=6 117. 2x=√1+3

2√1+3x (*)

118. 2x=√3+1

2√3+ 2√3+

1

2√x+3 (*)

119. x2−4x −3=√x+5 120. √3x+1=−4x2+13x −5 121. 2x=√37+√3 x+7

8

123. 2√3x −2+5√x+1=12 124.

√x+7−√x=1 (L-96) 125.

√2− x=1−√x −1 (TCKT-00) 126.

√17− x2−√32x2−1=1 127.

√x −2+√x+1=3 128. 10√x3

+1=3(x2+2) 129. 10√x6+1=3(x4+2) 130. 7√x3−1

=2x2+5x −1 131. √x

3 +8 x2

+8 =

1

132. x2 2x 2x 1 3x24x1 133. 5x2 14x 9 x2 x 20 5 x1 134. 8x2−3√8x3+1+3=2x

135. 2x3+(x −2)√2x3+5x2+5x+3=4x2+x −2 136. 2x2

+x+3=3x√x+3 137. √x+8=3x

2

+7x+8

4x+2

138. 15x2+2(x+1)√x+2=2−5x 139. 2(1− x)√x2+2x −1=x2−2x −1 140. (4x −1)√x2+1=2x2+2x+1 141. x+2+x√2x+1

x+√2x+1 =√x+2

142. (√x+3−√x+1)(x2+√x2+4x+3)=2x (*) 143. 4x2+3x+3=4x√x+3+2√2x −1

144. 4√x+3−√x −1=x+7

145. 2x√x2− x+1+4√3x+1=2x2+2x+6

146. 6√2x+4−4√x+1=x+8 147. 10√2x+2+2√x+3=x+23 148. 8x2

+3x+7=6x√x+8 149. 2x√x+4=3x2+3x −3

150. (x+3)√x+3+3√x+3=8x3+12x2+3x −9 151. √2x −3+√5−2x+4x − x2−6=0

152. √2x −3+√5−2x=3x2−12x+14 153. √x −2+√4− x=2x2−5x −1 154. √314− x3

+x=2(1+√x2−2x −1) 155. √x+√x+1+√x2+x=1

156. √x+4+√x+√1− x=3 157. 2√1− x+√x=√2− x 158. 2x+√2− x2+√42− x4=4

159. √x2−2x+5+√x −1=2 (NN-99) 160. 2011√4x −1+1987√4x2−1=2011 161. 2+√x

3+√1− x=√x+√1− x 162. √x+3+√− x2+3x −2=2 163. √x+4−√2x+3=x −1

164. (x −1)√x+1+√2x+1=√x+2 165.

x2+√x+5=

1

x+√2x+4 166. 2+√x+6=√2x+5+√x+3 167.

√x+8+√x+4=√2x+3+√3x 168.

√x+3+√32x+4=√52x+2+√33x+3 169