CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 1 CHUYÊN ĐỀ HỆ PHƯƠNG TRÌNH BÀI TẬP GIẢI HỆ PHƯƠNG TRÌNH ĐỐI XỨNG (PHẦN 1) Bài 1. Giải các hệ phương trình sau trên tập hợp số thực 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4, 1, 2. 2, 2, 164. 5 3, 3, 3 5. 8, 4, 5. 2, 5, 1. 208, 6, 96. 55, 7, 24. 7, 8, 3. 2 9, x xy y xy x y x y x y x xy y x y xy x y x y xy x y x y x y xy x y x y xy x y xy x y xy x y xy x  + + =  + + =  − =   + =   − + = −  + + =   + + + =  + + =   + − + =  + = −   + =  =   − =  =   + + =   + − =   ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1, 0. 2, 10, 1. 1, 11, 1. 1, 12, 3. 3 3 7 13, 13, 5 7. 2 2 , 14, 6. 5 5 , 15, 1. 16, y xy x y xy x y x y xy x y x y xy xy x y x xy y x y xy x y xy x y xy x y xy x y x y xy x y x y xy x y x  + − =   + =    + − + =  + − = −   + − =  = + −   + + =  − − =   + + =  + + =   + = +   + =    + = − + +  + − =  + + 2 2 3, 2. y x y y x =   + =  ( ) ( ) ( ) ( ) 2 2 3 3 3 3 3 3 3 3 3 3 2 2 2 2 3 3 4, 17, 4, 1, 18, 7, 5, 19, 35, 2, 20, 2, 4, 21, 2, 7, 22, 2. 3 3 , 23, 160. 5 3, 24, 2. x y xy xy x y x y x y x y x y x y x y xy x y x y x y xy x y x y x y y x x y xy x y x y xy x y x y  + + =   + + + =   + =   + =  + =   + =   + =   + =    + + + =   + =    + =   + = −   + =   + =  + = + − + = 2 2 3 3 2 2 2 2 2 2 4 2 2 4 2 2 4 2 2 4 2 2 5, 25, 2. 11, 26, 1. 4, 27, 2. 2 3 2, 28, 14. 7, 29, 21. 5, 30, 13. 5, 31, 13 x y xy xy x y x xy y x xy y x xy y x xy y x xy y x y x xy y x x y y x y x x y y x y xy x y xy       + + =   + =   + + =   − + =   + + =  + + =   + + = +   + =    + + =   + + =    + =   − + =   − − = + + = 3 3 . 2 2, 32, 8. x y xy x y    + + =   + =  CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 2 Bài 2. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( )( ) ( )( ) 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 30, 1, 35. 2, 2, 2. 7, 3, 2. 11, 4, 6 6 11. 18, 5, 1 1 72. 1 2 , 6, 1 1 . 1 1 5, 7, 1 1 x y xy x y xy x y x y x y xy x y x y xy xy x y x y x y xy x y x y x y xy x y xy xy x y x y x y x y  + =   + =    − = −   − =    − =   − =   + + =    + + =    + + + =   + + =    + + = +   − + = −   + + + = + + + = ( ) 2 2 3 3 2 2 4 2 2 4 4 4 6 6 2 2 2 2 9. 2, 8, 2. 10, 9, 73. 1, 10, 1. 1 13, 11, 1 12. 1 1 4, 12, 1 4. 7 5, 13, 1. 1 x y x y x y x x y y x y x y x y xy xy y x x y xy xy y x x y xy x y xy xy xy x y xy x y xy         + =   + =    + =   − + =    + =   + =    + + + =     − − + =      + + =        +  + + =    + = −  + = +  2 2 4 4, 4, 5 3. x y x y xy x y xy  + = + + −  + = −  ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 2 , 1 1 3 15, 1 1 6. 15, 16, 85. 1 1 6, 17, 1 1 18. 1 1 9, 18, 1 1 27. 19, x y y x x y xy x y x y y x x y x y y x x y xy x y xy x y xy x y xy x y  + =  + +      + + =          + + =           + + =          + + =           + + =          + + =           + + =       + ( ) ( ) 2 2 2 3 3 2 2 3 2 2 2 2 2 2 4 , 1 1 4. 1 1 1 1 4, 20, 1 4 . 1 1 5, 21, 1 4. 10 , 3 22, 5. 20, 23, 1 1 5 . 4 3 , 24, 1 1 x y xy y x x y x y x x y y x y x y xy y x y xy xy xy x y x y x y x y x y x y y x x y x y x y xy xy x y  + + =   + + + =      + + + =        + + + =     + + =         + =   + −  + =  − +   + =   + =   + =   + + = + − 1.    =   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 3 Bài 3. Giải các hệ phương trình sau trên tập hợp số thực 2 2 2 2 2 2 2 2 2 2 2 2 3, 1, 3 1. 4 4, 2, 5 5 8. 3 1, 3, 3 3 5. 1, 4, 2. 7, 5, 13. 3 , 6, 1 1 1. 2, 7, 1 1 4. 8, x y xy x y xy x y xy x y x y x y x y xy x y xy x y xy x y x xy y x xy y x y x y xy xy x y x y y x x y x y + + =   + − = −  − − = −   + − + = −   + + + − =  + = +  − + =   + =  + + =   + + =   + + =   + = +    + =     + + + =   ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 , 2 1 1 3 1. 3 , 9, . 1 1 1 3, 10, 2 2 6. 1 13, 11, 1 12. 12, 12, 13. 7, 13, x y y x xy x y x y xy x y x y xy x y x x xy x y x y xy x y x y xy xy xy x y xy xy y x x y xy x y xy x y x y x y x  + =  + +   = + +   + + =   + − =    + + =    + +  + =    + + + =     − − + =   − =   + =   − − = + + ( ) 2 2 2 175. 4 2, 14, 2 . y x y xy x y xy    =    + − =  = −  ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 4 4 2 2 2 2 2 2 2 2 2 2 3 3 2 2 3 3 3, 15, 17. 18, 16, 1 1 72. 4 4 10, 17, 4. 3 3 8, 18, 3 3 4. 3 , 19, 15. 2, 20, 1. 2, 21, x xy y x y x x y y x x y y x y y x xy x xy y x y xy x y x y x y x y x y x y x y x y xy x y x y  + + =   + =    + + + =   + + =    + + + =   + + =    − + − =   − − =    − =  −   + + =  + =   +  =  +  − = − ( ) 3 3 4 4 4 4 9 9 2 2 2 2 4 4 2 2 2 2 2 2 2 6. 1, 22, 1. 1, 23, 1. 12, 24, 1 . 3 82, 25, 3. 2, 26, 1. 2 , 27, 2 . 7 7 16 , 28, 6 2. 29, x y x y x y x y x y x y y x x y xy x y xy x y xy x y xy x y xy x y x y xy x y xy x y xy    − + =    + =   + =    + =   + =    + =     + =    + =  =   + =  =  + =   + =   + + + =   + = −   + = 2 2 2, 4 . x y x y xy     + + + =  CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 4 Bài 4. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( )( ) ( ) 3 3 2 3 3 3 3 2 2 2 2 2 2 4 4 4 2 2 4 2 2 3 3 3 3 5, 1, 1 1 35. 4, 2, . 1 1 5, 3, 1 1 22. 1 1 4, 4, 1 1 4 . 78, 5, 97. 481, 6, 37. 1 7, xy x y x y x x y y x xy y x y x y x y x y x y x y x y xy x y xy x y x x y y x xy y x y x y + + =    + + + =    + + =    + =   + + + =     + + + =    + + + =    + + =   + =   + =    + + =   + + =   + + = 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 2 2 2 2 7, 5. 2, 8, 3. 3 3 9, 9, 3, 3 5 , 10, 4 3 . 4 4 10, 11, 2 4. 2 9 9 , 12, 3 3. 2 3 2 , 13, 2 3 x y xy x y y x x y xy x y xy x y xy x y xy y x y y xy x x x xy y y x x y x y xy y x y x x y y xy y y x x y   + + =   + =    + + =   + + + + =  + + =   + + =   − =    + + + =     + =    − + + =   − + =   − = − − 2 .x y    =   ( ) ( ) ( ) 3 3 2 2 3 3 2 2 3 3 3 3 3 3 2 2 2 2 3 3 2 2 3, 14, 3. 5, 15, 2 4. 2, 16, 3 8. 1 1 4, 17, 1 1 4. 2, 18, 3 3 5 2. 3 1, 19, . 20, x y xy x y xy x y x y xy x y xy x y x y xy x y x y x y x y x y xy x y xy x y xy x y xy x y x y x  + + =   + + =    + + + + =   + + =    + =   + + + =    + + + =     + + + =    + =   + − =    + = −   + = +   ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2, 2 . 3 1 , 21, 3 4 . 4 2, 22, 1, 3 2 2, 23, 3 9 6 4 3. 2 2 , 24, 2 4 4 2 . 3 2, 25, 2 . 1 26, x y y y x y y xy y y x y y x y xy x y xy x y x x y y x y x x x y x y y x y x x y y x x y x xy y x y +  − + =    − =   − + =   − =    + = −   + + = + +    + + =    +  + + + + =    + + =   + + + =    + = +  + =  + = + 5 , 1 5 . 2 1, 27, 1 3 1. x xy y x xy y y x x   + + =  = +   − + =   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 5 Bài 5. Giải các hệ phương trình sau trên tập hợp số thực ( )( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1, 1, 2 2 2 3. 2 2 1, 2, 2 3 2 4 . 1, 3, 2 3. 5 2 2 26, 4, 3 2 11. 2 2 1 0, 5, 4 4 4 1 0. 4 1, 6, 2 4 2. x xy y x x y xy x xy y x x y xy x y x x y x xy y x x y x y x y x x xy y x x y x x y  + + =   + + + =    − + =   + = + +    + =   + = +    + + =   + + − =    − − + =     − + − + =    + =   + = +   ( ) ( ) 2 2 3 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 , 7, 2 3 . 5 2 2, 8, 3 9 2 2 7. 2 5 2 1 , 9, 4 2 2 5. 2 2 1 , 10, 2 4 4 6. 2 2 2 1, 11, 9 16 4 . 2 12, x y xy y xy y xy y y x y xy x y y xy x y xy x y x xy y x y xy x y x xy x y x xy x x xy y x y  + + + + =   + + =    + + =   + + + =    + = −   + + + = +    + = +   − + = +    + = + +   + = + +   + = ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 , 8. 4 6 3 , 13, 4 2 4 . 10 10 5 18 9, 14, 2 4 1 . 4 4 2 , 15, 3 4 2 . 2 2 1, 16, 4 1 . x y x y xy xy y x x y x y xy x x y x y x y x y x y xy x y x y xy x x y y x y x  +  + + =  = +   + = +   + = + +   + + = +    + = +  + = +   − + + = −   + + =   ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 3 2 2 2 2 2 2 2 2 3 9, 17, 2 1. 4 2 4 13, 18, 2 2 1 1. 3 1 6 2 2, 19, 5 4 2 1. 3 6 , 20, 2 2 . 2 2 , 21, 2 1 . 1 1 22, y xy x x y y x y x xy x y x y y x y x x y xy y x xy y x x y xy x y xy y x y x x x y x y y x x x y + = +   + = +   + + = +   + = + +    + = + +   + − = +    + =   + − + = +    + − + =   + = + +   + + ( )( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 4 , 2 3 5 2. 4 2 4 , 23, 1 3 . 2 2 , 24, 2 4 4 . 4 5 4, 25, 3 2 5 2 . 5 7 4 3 , 26, 2 2 3 11. 1 27, x y y y xy y x x x x y x y x y xy x y xy xy x x y x y xy x y x x y xy x y xy x y x y x y x xy x y x y y  + + + =   + = + +    − + + + =    + = +   + = +   − + + = +    + + = + −  = + +   + + = +   − + + =   + + ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 3 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0, 2 3 . 2 3 1 14, 28, 3 9. 2 , 29, 2 . 1 2 , 30, 1 2 1 . 2 1 1 3 , 31, 2 2 3 . 1 3, 32, 1 3 . y x y xy y x xy x y y x x y x x x y x xy y x x xy y x y xy x y x x y y y y x x y x x y xy y x y y x y x − =   + + + + + =    + − =   + + =    = + +   + = +    − + + = +   + − = +    − + = +   = − +    − = +   + = +   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 6 Bài 6. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 4 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 1 4 2 4 , 1, 1 5 2 . 2 1 2 , 2, 2 . 2 , 3, 1 1 . 1 3 1, 4, 4 . 1 2 , 5, 2 1. 1 2 , 6, 1 2 x y y y xy xy y y x xy x x xy x y x y y x x x y x x xy x y x x xy y x y x y x y x xy y x xy x x xy y x y  + + = +   + = +    − + =    = + +   + + − =   + − =    + + = + +   + + =    + = + +   − = −   = + + = ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 3 2 2 2 2 2 . 2 4 2, 7, 4 2 1. 1 2 , 8, 1 2 3 . 3 8 4 3, 9, 5 10 2 2 7. 3 9 5, 10, 3 3 3. 2 1 1, 11, 5 4 5 . 2 3 2 12, xy y x xy y y x x xy x x x x y x x xy y x xy x y xy x y xy x y x x y y xy x xy x y x y x x y   +  + + =   + + =   + − =   + = + +    − + =   − + = +    + = +   + − =    + + + − = +   + − = +   − + = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 7, 2 4 4 2 1. 1 4 , 13, 1 2 . 2 3 3 , 14, 2 3 1 . 3 5 1, 15, 3 1 3 . 2 2 7 , 16, 3 1 1 8 3. y x xy y x x y y x y x x y y x xy y y x x y y x xy y y y x x y y x y y x x y x y  +   − + = +    + + + =   + + − =    + + = +   + − − =    + = + +   + − − =    + + + =   − + + + = −   ( ) ( ) 4 3 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 1 , 17, 3 4 4 3 2 . 3 2 3 2, 18, 2 2 5. 2 2 1, 19, 2 2 1. 1 2, 20, 1. 3, 21, 2 3 3 7. x x x y y x y x xy x x y x y x x xy y x y xy x xy y xy x y y x xy y x y x y x y y xy x x y x xy y x xy y  + + + + + = + + +   + + = + +    − + − + = +   − + =    + = + +   + − = + +    + = + + +   + = + +    − + =  + = + ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 1 2 5 4 3, 22, 2 1 1 2 . 1 1, 23, 2 4. 2 3 7, 24, 2 4 4 5 0. 2 3 4 , 25, 3 2 . 2 2 4, 2 26, 2 . 3 2 2 1 27, xy x x y x y y x x x y x y y x x y y x y x y x xy x y x y x x x y x y y x x y x y x y y x y    −  − + =    + = + +   + − =   + = +    + = +   − − + =    + − + =   − − =  −   + − + = +  −   + = + +  + = − + − ( )( ) ( ) ( ) ( ) 2 2 2 2 2 5, 2 3 2 . 2 2 1 2 1 1, 28, 2 2 2 1. 2 2 1, 2 29, 2 1 . 1 5 1, 30, 4 3 1 . x y x y x y y x y x y x y x x y x y y x y y x x y x xy x y x x y     + −  + + =  − −   + − − = +   − + + = + +   −  + − =  −   − −  =  − +  + = +   − +  =   . MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THI T GIÁP 1 CHUYÊN ĐỀ HỆ PHƯƠNG TRÌNH BÀI TẬP GIẢI HỆ PHƯƠNG TRÌNH ĐỐI XỨNG. BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 3 – QUÂN ĐOÀN TĂNG THI T GIÁP 2 Bài 2. Giải các hệ phương trình sau trên tập hợp số thực