BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ -0985.873.128 1. 126 22 =−+ xx (VH-98) 2. 3111 22 =++ xx 3. 2381716 −=+ xx (QG-D-97) 4. xxx −=−− 1251 2 (TCKT-97) 5. 02193 2 =−++− xxx 6. )4(382 2 −=−− xxx (BD-01) 7. 94)3( 22 −=−− xxx (Y HCM-01) 8. 1266 2 −=+− xxx (XD-01) 9. 14 2 =++ xxx (HVCTQG HCM-00) 10. 1223 2 −=+− xxx 11. 231034 −=−− xx (HSGQG-01) 12. 1313 −=++ xx 13. 4235 +=++− xxx (HH-98) 14. 31243 +=−−+ xxx (NH-98) 15. 36333 22 =+−++− xxxx (TM-98) 16. 53322 −=−−+ xxx (BK-94) 17. 42533 −=−−− xxx (A05) 18. 3200820098 22 ++−=+ xxx 19. 411222 =+−+++ xxx (D05) 20. 811 +−=−+ xxx 21. 333 3221 −=−+− xxx (Đề 113) 22. 1334 33 =−−+ xx (Đề 12) 23. 333 511 xxx =−++ 24. 333 121216 −=+− xxx 25. 2 2)2()1( xxxxx =++− (SP2-A00) 26. x x xx x 11 1 1 − =−−− 27. 221682 22 +=−+++ xxxx 34. 322323 22 −++−=+++− xxxxxx 35. xxxxxxxx 32222 2222 +++=+++ 36. )17)(1()6)(1(3)72)(1( +−=−−++− xxxxxx 37. xxxxxxx 223233 2223 +++=++++ 38. 111 32 ++=+−++ xxxxxx 39. 111 2422 +++=+−+++ xxxxxxxx 40. 322323 22 −++−=+++− xxxxxx 41. 13 2 2 11 1 =++−+++ x xx xx x 42. 37221223 2 +++=+++ xxxxxx 43. 2352122 3 2 =−+−−+ + xxxx x x 44. 3 8 28 3 24 2 + + ++=++ + + x x xxxx x x 45. 3 2 3 3 2 3 1 xxxxx ++=++ 46. 11 4 23 4 =+−++ xxxx 47. 22 22 2 22 2 = +− − + ++ + x x x x 48. xx x x −=−− − 123 23 2 (Đề 124) 49. 2 2 1 2 1 1 2 33 =++ + xx x (GT-95) 50. xxxx 4342 32 +=++ 51. 22 291 xxx +−=+ 52. 11 4 5 1 4 5 2222 +=−−−+−+− xxxxx 53. 21212 =−−−−+ xxxx (BCVT-00) 54. 2 3 1212 + =−−+−+ x xxxx (TCKT-95) 55. 211 2 4 2 =−++−− xxxx 28. 0)1(12 2 =−+−−−− xxxxxx 29. 62)22(3 ++=−+ xxx (KTQS-01) 30. 342123 2 +++=+++ xxxxxx 31. 1 1 2 21 = + + ++−+ x x xx 32. ( ) ( ) 1111 22 =−+++ xxxx 33. xxxx 33)2)(5( 2 +=−+ 56. 713 22 =+−−− xxxx 57. 43132 22 +=+−+ xxxx 58. xxxx −=+++ 91232 22 59. 2242 22 −=+−− xxxx 60. xxxx 6235352 22 −=+++ 61. 1952252 22 =−++++ xxxx 62. 12824484 222 ++=+++++ xxxxxx 63. 36333 22 =+−++− xxxx (TM-98) 64. 123 22 =−+−+− xxxx (NT-99) 65. 0221)2( =+−−− xxx (*) 66. 1)1( 4 29 1 2 −−=−+ xxxx (*) 67. 999 2 ++−=−+ xxxx (*) 68. )121(11 22 xxx −+=−+ 69. 8)6)(2(62 =−++−++ xxxx 70. 41211 2 =−+++− xxx 71. 4)5)(2(52 =−++−++ xxxx (CĐBK-06) 72. 5)4)(1(41 =−++−++ xxxx (NN-01) 73. 22 4324 xxxx −+=−+ (MĐC-01) 74. 11 2 =+−++ xxxx (ĐHHP-00) 75. 234413 2 −=−−−−+− xxxx (ĐHHP-01) 76. 2 31 1 = − + − x x x x (ĐHTL-01) 77. 224222 2 +−−=+−− xxxx (CĐSP-01) 78. xxxxx 32312 2 +=−+++ 79. 93232 222 =+++++ xxxxx 80. 7109223522 2 −+++=+++ xxxxx 81. )13)(4(241341 +++=++++ xxxxx 95. x xxxxx 4 262 22 +=+++++ 96. 52321252 22 +=+++++ xxxxx 97. 11 22 ++=++ xxxx 98. xxxx ++=++ 22 11 99. 3 33 3 211 ++=+++ xxxx 100. xxxxx 3112 22 =+−+++ 101. 1)1()1( 3 2 3 3 2 =++++ xxxx 102. 3)4(20)5( 3 23 2 3 2 =−+−−−+ xxxx 103. 119)13()13( 3 2 3 2 3 2 =−+−++ xxx 104. 3318)3()6( 3 2 3 2 3 2 =−−−−++ xxxx 105. 444 121 +=++ xxx 106. 22 )2(2 xx −=− 107. 1000800011000 2 =+−− xxx 108. 3 3 2 1 12 + += x x 109. 3 3 2332 −=+ xx 110. 3 3 1221 −=+ xx 111. 255336853 23 3 −+−=− xxxx 112. 16 152 588 2 + =−+ x xx 113. 28 94 77 2 + =+ x xx 82. 253294123 2 +−+−=−+− xxxxx (QS97) 83. 93232 2 =+++++ xxxxx 84. 1313214 2 +=+−++ xxxxx 85. )3(43262 2 ++=+++ xxxxx 86. )2(3422 2 xxxx −+=+− 87. xxxx 51)34(41 2 =−−++ 88. )3(4326 2 ++=+−++ xxxxxx 89. 1212 2 =+++++ xxxxx 90. 41292 22 +=+−+++ xxxxx 91. 211 22 =+−+++ xxxx 92. xxxxx 211 22 ++−=++ 93. 113 +=−−+ xxx 94. 41292 22 +=+−+++ xxxxx 114. 11 2 =++ xx (XD-98) 115. 615 =−++ xx 116. xx 31 2 3 12 ++= (*) 117. 3 2 1 3 2 1 3 2 1 32 ++++= xx (*) 118. 534 2 +=−− xxx 119. 513413 2 −+−=+ xxx 120. 3 3 8 7 72 + += x x 121. 08563232 3 =−−+− xx (A09) 122. 121522 3 =++− xx 123. 17 3 =−+ xx (L-96) 124. 112 3 −−=− xx (TCKT-00) 125. 11217 3 2 4 2 =−−− xx 126. 312 3 =++− xx 127. )2(3110 23 +=+ xx 128. )2(3110 46 +=+ xx 129. 15217 23 −+=− xxx 130. 3 1 8 8 2 3 = + + x x 131. xxx 231838 32 =++− 132. 243552)2(2 2233 −+=+++−+ xxxxxxx 133. 3332 2 +=++ xxxx 134. 24 873 8 2 + ++ =+ x xx x 135. xxxx 522)1(215 2 −=+++ 136. 1212)1(2 22 −−=−+− xxxxx 137. 1221)14( 22 ++=+− xxxx 144. 23322210 +=+++ xxx 145. 86738 2 +=++ xxxx 146. 33342 2 −+=+ xxxx 147. 93128333)3( 23 −++=++++ xxxxxx 148. 0642532 2 =−−+−+− xxxx 149. 141232532 2 +−=−+− xxxx 150. 15242 2 −−=−+− xxxx 151. )121(214 2 3 3 −−+=+− xxxx 152. 11 2 =++++ xxxx 153. 314 =−+++ xxx 154. xxx −=+− 212 155. 4222 4 42 =−+−+ xxx 156. 2152 2 =−++− xxx (NN-99) 157. 11414 2 =−+− xx 158. xx x x −+= −+ + 1 13 2 138. 2 12 122 += ++ +++ x xx xxx 139. xxxxxx 2)34)(13( 22 =++++−+ (*) 140. 12234334 2 −++=++ xxxxx 141. 7134 +=−−+ xxx 142. 62213412 22 ++=+++− xxxxxx 143. 814426 +=+−+ xxx 159. 2233 2 =−+−++ xxx 160. 1324 −=+−+ xxx 161. 2121)1( +=+++− xxxx 162. 42 1 5 1 2 ++=++ x x x x 163. 35262 +++=++ xxx 164. xxxx 33248 4 ++=+++ 165. 3535 3322423 +++=+++ xxxx 165A. 33 3 23 2 20102009620107320093 =+++−−+− xxxxx BÀI TẬP HỆ PHƯƠNG TRÌNH Giải các hệ phương trình sau : 1. + + = − − + = − 2 2 1 ( 99) 6 x xy y MTCN x y y x 2. + = − − + = 2 2 4 2 2 4 5 ( 98) 13 x y NT x x y y 3. + = − + = 2 2 3 3 30 ( 93) 35 x y y x BK x y 4. + = − + = + 3 3 5 5 2 2 1 ( 97) x y AN x y x y 5. + + = − + + = 2 2 4 4 2 2 7 ( 1 2000) 21 x y xy SP x y x y 6. + + = − + + + = 2 2 11 ( 2000) 3( ) 28 x y xy QG x y x y 7. ( ) =−− =++++ 6)1)(1( 3)1(1 22 yx yyxx 8. ( )( ) =++++ =++ 17)1()1( 811 xyyyxx yx 9. −=+− −=++ )(6 )(7 22 222 yxyxyx yxyxyx 15. =−+ =++ 2222 2222 3 yxxyyx yxxyyx 16. + + = − + + = 2 ( 2)(2 ) 9 ( 2001) 4 6 x x x y AN x x y 17. + + = − + + − = 2 (3 2 )( 1) 12 ( 97) 2 4 8 0 x x y x BCVT x y x 18. + = − + + = 2 2 3 3 4 ( 2001) ( )( ) 280 x y HVQHQT x y x y 19. + + = − + + = 2 2 2 2 1 ( )(1 ) 5 ( 99) 1 ( )(1 ) 49 x y xy NT x y x y 20. ( ) = ++ +=+ 24 1 1 )1(2)1( 22 22 22 yx yx yxxy 21. + + + = − + + + = 2 2 2 2 1 1 4 ( 99) 1 1 4 x y x y AN x y x y 10. =−− =−−+ 36)1()1( 12 22 yyxx yxyx 11. =+++ =+ 4 11 2 yx yx x y y x 12. =+++ =+++ 4 4 22 x y y x yx x y y x yx 13. =−+ =++ 1 11 3 22 xy yx xyyxyx 14. ++= = + + + 13 2 1 2 )1( 2 2 )1( 2 yxxy x y y x 22. =++ = + + + 6) 1 1)(( 3 2 11 22 xy yx y y x x 23. =+++ =+++ 4 1 622 22 y x x y xy xy xyxyxyyx 24. = ++ =+ 5 1 1)( 4 1 xy yx xy xy 25. = ++ = ++ 18 1 1)( 6 1 1)( 2 22 xy yx xy yx 26. = ++ = ++ 27 1 1)( 9 1 1)( 3 33 2 22 xy yx xy yx 27. −=− −=− 232 232 22 22 xyy yxx (QG-00) 28. −= −= xyy yxx 3 3 2 2 (MTCN-98) 29. += += xyy yxx 23 23 2 2 30. += += x x y y y x 1 2 1 2 2 2 31. = + − = + 3 3 3 8 ( 98) 3 8 x x y QG y y x 39. − = − = 2 2 1 2 1 2 x x y y y x 40. −=+ −=+ 22 22 22 22 xyxy yxyx 41. =−− −=++ 732 13 22 22 yxyx yxyx 42. =+ =+ 5 10 23 23 xyy xyx 43. =+− −=+− 133 13 22 22 yxyx yxyx 44. =− =− 19 2)( 33 2 yx yyx 45. =++ =−− 15))(( 3))(( 22 22 yxyx yxyx 55. +=+ =++ yxyx yxyx 3 1 33 22 56. ++=+ −=− 2 3 yxyx yxyx 57. =+ −=− 4 263 22 2 yx xyxyy 58. =++ =++ 3 42 2 2 xxyx yxyx 59. =++ =++ 75 522 2 2 xxyy yxyx 60. =++− =++ 945 3 2 22 yxxyy xyyx 61. −+=+ =++ 9572 3 2 22 yxxyx xyyx 32. += += xyy yxx 2 2 3 3 33. += += xyy yxx 5 5 3 3 34. −= −= 12 12 3 3 xy yx 35. += += 223 223 23 23 xyy yxx 36. + = − + = 1 3 2 ( 99) 1 3 2 x y x QG y x y 37. =+ =+ 2 2 3 2 3 2 y xy x yx (TL-01) 38. + = + = 2 2 2 2 2 3 2 3 y x x x y y 46. =++ =−− 175))(( 7))(( 22 22 yxyx yxyx 47. =++ =++ 422 42 22 22 yxyx yxyx 48. =− =+ xyx xyx 33 33 2 2 49. =+ =+ xyxy yxyx 32 2 2233 50. =+− =++ 122 222 222 222 xyyxyx xxyx 51. =++ =+ 222 22 31 2)1( xxyyx yx 52. =+ =+ 3333 3 32 2 yxyx xyyx 53. += =−+ yxx xyyx 3 22 2 1 54. +=+ =++ xyyx yxyx 22 3 33 22 62. =−−++ =+ 22 2 22 22 xyyxxyyx yx 63. =+ =+ 32 32 2 2 yxx xyx 64. =+ =+− 2 44)1( 22 2 yx yyx 65. += −=− 12 11 3 xy y y x x (A-03) 66. −=+++ −=++++ 4 5 )21( 4 5 24 232 xxyyx xyxyyxyx (A-08) 67. +=+ +=++ 662 922 2 2234 xxyx xyxyxx (B-08) 68. −=−− −=++ xxxyyx yxyxxy 2212 2 22 69. =+−+−− −+= 01681645 )4)(45( 22 2 yxxyxy xxy 70. =−++ =+++ yxyx yxyyx )2)(1( 4)(1 2 2 71. = + + = + +++ 3 )( 1 2 7 )( 3 )(44 2 22 yx x yx yxxy 72. =−−+ =−− 3342 1623 22 yxyx yxxy 73. =− =+ 6)2( 8)32( 3 3 yx yx 74. =+ =+− 1 32 22 22 yx xyx 81. =+++ =+++ 4 11 4 22 22 y x x y yx xyyxyx 82. =+ +=+ 13 )1()1( 22 22 yx yxxy 83. −−= ++−= 262 43 3 3 yyx xxy 92. =−−+−− =+ 3354 43 yxyx x y y x 93. =−++ =−++ 8 4 2222 yxyx yxyx 94. =+ =++ 4 282 22 yx xyyx 95. =+ +=+ 6 )(3)(2 3 3 3 2 3 2 yx xyyxyx 75. =+ =+ 162 2 1 23 22 xyx yx 76. =+ =+ 13 3 22 23 yx yxyx 77. = + ++ = ++ 4 1 4 1 1)( 22 xy yx xy xy xy yx 78. = ++ =++−+ 8 1 1)( 02)62( 2 22 xy yx xyyxxy 79. =++ =++ 3 1 4 1 2 2 x xyx x yx 80. =++ =++ 3 11 42 2 2 y x xy x xyxyyx 84. += +− + += +− + xy yy xy y yx xx xy x 2 3 2 2 3 2 92 2 92 2 85. ++=+ ++=+ 321 321 xy yx (*) 86. =+++ =+++ 11 24 yyy yxx 87. =++ =++ 11 24 4 4 yx yx 88. =+−+++ =− 524352 32 yxyx yx 89. =++ =+ 17 7 22 xyyx yx 90. −+=+− =++ 33223 35 yxyx yx 91. −=+− +=+ 222 1 2 yyx xyx 96. + = + − + = 7 1 ( 99) 78 x y y x xy HH x xy y xy 97. = =+ 9 3 411 xy yx 98. =−+ =−+ 22 22 xy yx 99. =++ =++ 224 224 xy yx 100. =++ =++ 11 11 xy yx 101. =−++ =−++ 479 479 xy yx 102. + + − = − + + − = 5 2 7 ( 1 2000) 5 2 7 x y NN y x 103. =+++ =++++ 71312 722 yx yxyx 104. =+++ −+−+−=+++++ 80 531531 22 yxyx yyyxxx 105. =+++++++ =+++ 61111 311 yxxyyx yx 106. + + + + + + + + + = − + + + − + + + + − = 2 2 2 2 1 1 18 ( 99) 1 1 2 x x y x y x y y AN x x y x y x y y 107. Giả sử hệ =++ =++ 1 2 222 zxyzxy zyx có nghiệm (x, y, z): CMR : 3 4 ,, 3 4 ≤≤− zyx . 33248 4 ++=+++ 165. 3535 3322423 +++=+++ xxxx 165A. 33 3 23 2 20102009620107320093 =+++−−+− xxxxx BÀI TẬP HỆ PHƯƠNG TRÌNH Giải các hệ phương trình sau : 1. + + = − − + = − 2 2 1 ( 99) 6 x xy y MTCN x y y x 2. +. BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ -0985.873.128 1. 126 22 =−+ xx (VH-98) 2. 3111 22 =++ xx 3. 2381716 −=+ xx (QG-D-97) 4. xxx. + + − + + + + − = 2 2 2 2 1 1 18 ( 99) 1 1 2 x x y x y x y y AN x x y x y x y y 107. Giả sử hệ =++ =++ 1 2 222 zxyzxy zyx có nghiệm (x, y, z): CMR : 3 4 ,, 3 4 ≤≤− zyx