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