Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128 BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ 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 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 +=−+ 34. 126 22 =++ xx (VH-98) 35. 322323 22 −++−=+++− xxxxxx 36. xxxxxxxx 32222 2222 +++=+++ 37. )17)(1()6)(1(3)72)(1( +−=−−++− xxxxxx 38. xxxxxxx 223233 2223 +++=++++ 39. 111 32 ++=+−++ xxxxxx 40. 111 2422 +++=+−+++ xxxxxxxx 41. 322323 22 −++−=+++− xxxxxx 42. 3 2 12 11 1 +++=+++ x xx xx x 43. 37221223 2 +++=+++ xxxxxx 44. 3522122 3 2 −++=−+ + xxxx x x 45. 3 8 28 3 24 2 + + ++=++ + + x x xxxx x x 46. 3 2 3 3 2 3 1 xxxxx ++=++ 47. 4 23 4 11 xxxx ++=++ 48. 22 22 2 22 2 = +− − + ++ + x x x x 49. xx x x −=−− − 123 23 2 (Đề 124) 50. 2 2 1 2 1 1 2 33 =++ + xx x (GT-95) 51. xxxx 4342 32 +=++ 52. 22 291 xxx +−=+ 53. 11 4 5 1 4 5 2222 +=−−−+−+− xxxxx 54. 21212 =−−−−+ xxxx (BCVT-00) 55. 2 3 1212 + =−−+−+ x xxxx (TCKT-95) 56. 211 2 4 2 =−++−− xxxx 57. 713 22 =+−−− xxxx 58. 43132 22 +=+−+ xxxx 59. xxxx −=+++ 91232 22 60. 2242 22 −=+−− xxxx 61. xxxx 6235352 22 −=+++ Tài liệu bồi dưỡng Đại số 10 1 Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128 62. 12824484 222 ++=+++++ xxxxxx 63. 1952252 22 =−++++ xxxx 64. 36333 22 =+−++− xxxx (TM-98) 65. 123 22 =−+−+− xxxx (NT-99) 66. 0221)2( =+−−− xxx (*) 67. 1)1( 4 29 1 2 −−=−+ xxxx (*) 68. 999 2 ++−=−+ xxxx (*) 69. )121(11 22 xxx −+=−+ 70. 8)6)(2(62 =−++−++ xxxx 71. 41211 2 =−+++− xxx 72. 4)5)(2(52 =−++−++ xxxx (CĐBK-06) 73. 5)4)(1(41 =−++−++ xxxx (NN-01) 74. 22 4324 xxxx −+=−+ (MĐC-01) 75. 11 2 =+−++ xxxx (ĐHHP-00) 76. 234413 2 −=−−−−+− xxxx (ĐHHP-01) 77. 2 31 1 = − + − x x x x (ĐHTL-01) 78. 224222 2 +−−=+−− xxxx (CĐSP-01) 79. xxxxx 32312 2 +=−+++ 80. 93232 222 =+++++ xxxxx 81. 7109223522 2 −+++=+++ xxxxx 82. 1)13)(4(24134 −+++=+++ xxxxx 83. 253294123 2 +−+−=−+− xxxxx (QS97) 84. 93232 2 =+++++ xxxxx 85. 1313214 2 +=+−++ xxxxx 86. )3(43262 2 ++=+++ xxxxx 87. )2(3422 2 xxxx −+=+− 88. xxxx 51)34(41 2 =−−++ 89. )3(4326 2 ++=+−++ xxxxxx 90. 1212 2 =+++++ xxxxx 91. 41292 22 +=+−+++ xxxxx 92. 211 22 =+−+++ xxxx 93. xxxxx 211 22 ++−=++ 94. 113 +=−−+ xxx 95. x xxxxx 4 262 22 +=+++++ 96. 41292 22 +=+−+++ xxxxx 97. 52321252 22 +=+++++ xxxxx 98. 11 22 ++=++ xxxx 99. xxxx ++=++ 22 11 100. 3 3 3 3 211 ++=+++ xxxx 101. xxxxx 3112 22 =+−+++ 102. 1)1()1( 3 2 3 3 2 =++++ xxxx 103. 3)4(20)5( 3 2 3 2 3 2 =−+−−−+ xxxx 104. 119)13()13( 3 2 3 2 3 2 =−+−++ xxx 105. 3318)3()6( 3 2 3 2 3 2 =−−−−++ xxxx 106. 444 121 +=++ xxx 107. 22 )2(2 xx −=− 108. 1000800011000 2 =+−− xxx 109. 3 3 2 1 12 + += x x 110. 3 3 2332 −=+ xx 111. 3 3 1221 −=+ xx 112. 255336853 23 3 −+−=− xxxx 113. 16 152 588 2 + =−+ x xx 114. 28 94 77 2 + =+ x xx 115. 11 2 =++ xx (XD-98) 116. 615 =−++ xx 117. xx 31 2 3 12 ++= (*) 118. 3 2 1 3 2 1 3 2 1 32 ++++= xx (*) 119. 3 3 8 7 72 + += x x 120. 534 2 +=−− xxx 121. 513413 2 −+−=+ xxx 122. 08563232 3 =−−+− xx (A09) 123. 121522 3 =++− xx 124. 17 3 =−+ xx (L-96) 125. 112 3 −−=− xx (TCKT-00) 138. 141232532 2 +−=−+− xxxx Tài liệu bồi dưỡng Đại số 10 2 Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128 126. 11217 3 2 4 2 =−−− xx 127. 312 3 =++− xx 128. )2(3110 23 +=+ xx 129. )2(3110 46 +=+ xx 130. 15217 23 −+=− xxx 131. 3 1 8 8 2 3 = + + x x 132. 3332 2 +=++ xxxx 133. 24 873 8 2 + ++ =+ x xx x 134. xxxx 522)1(215 2 −=+++ 135. 1212)1(2 22 −−=−+− xxxxx 136. 1221)14( 22 ++=+− xxxx 137. 0642532 2 =−−+−+− xxxx 139. 15242 2 −−=−+− xxxx 140. )121(214 2 3 3 −−+=+− xxxx 141. 11 2 =++++ xxxx 142. 314 =−+++ xxx 143. 2152 2 =−++− xxx (NN-99) 144. 11414 2 =−+− xx 145. xx x x −+= −+ + 1 13 2 146. 2233 2 =−+−++ xxx 147. 1324 −=+−+ xxx 148. 2121)1( +=+++− xxxx 149. 42 1 5 1 2 ++=++ x x x x 150. 35262 +++=++ xxx 151. xxxx 33248 4 ++=+++ 152. 3535 3322423 +++=+++ xxxx 154. xxxxxx 2)34)(13( 22 =++++−+ 155. 33 3 2 3 2 20102009620107320093 =+++−−+− xxxxx Tài liệu bồi dưỡng Đại số 10 3 Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128 BÀI TẬP HỆ PHƯƠNG TRÌNH Bài 1 : 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 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.      =−+ =++ 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 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 Tài liệu bồi dưỡng Đại số 10 4 Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128 15.      ++= = + + + 13 2 1 )1()1( 2 2 2 2 yxxy x y y x 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 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 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 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 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 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 Tài liệu bồi dưỡng Đại số 10 5 Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128 72.    =−−+ =−− 3342 1623 22 yxyx yxxy 73.      =− =+ 6)2( 8)32( 3 3 yx yx 74.      =+ =+− 1 32 22 22 yx xyx 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 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 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 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 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 Tài liệu bồi dưỡng Đại số 10 6 . xxxx 104 . 119)13()13( 3 2 3 2 3 2 =−+−++ xxx 105 . 3318)3()6( 3 2 3 2 3 2 =−−−−++ xxxx 106 . 444 121 +=++ xxx 107 . 22 )2(2 xx −=− 108 . 100 08000 1100 0 2 =+−− xxx 109 . 3 3 2 1 12 + += x x 110. 3 3 2332 −=+ xx 111. 3 3 1221 −=+ xx 112. 255336853 23 3 −+−=−. ++=++ 22 11 100 . 3 3 3 3 211 ++=+++ xxxx 101 . xxxxx 3112 22 =+−+++ 102 . 1)1()1( 3 2 3 3 2 =++++ xxxx 103 . 3)4(20)5( 3 2 3 2 3 2 =−+−−−+ xxxx 104 . 119)13()13( 3 2 3 2 3 2 =−+−++ xxx 105 . 3318)3()6( 3 2 3 2 3 2 =−−−−++. 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