81 phương trình có hướng dẫn.

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81 BÀI H PHƯƠNG TRÌNH  4xy + 4 x2 + y2 + 3 85 =   2 3 1. (x + y) 2x + 1 13 =  x+y  3 vn x − 2√3y − 2 = 2y − 3√2x − 1  3 2. 2y − 2 − 2√3y − 2 = x − 3√2x − 1 3 x − 2y + x = 7  3. y  2 x − 2xy − 6y = 0 √x + y + √x + 2y + 2 = 7  4. √  2x + 1 + √3y + 1 = 7  (2x − 1)2 + 4(y − 1)2 = 51 5. 6.  x2 + y2 = 10 th. xy (x − 1) (y − 2) = −20 2√x + 3y + 2 − 3√y = √x + 2 phương trình 1 gi i thoát  (x − 2) (2y − 1) = x3 + 20y − 28 7. phương trình 2 gi i thoát 2 √x + 2y + y = x2 + x  x3 + 2y2 = x2 y + 2xy 8. th x = y t 1 vào 2 đ t 2 n ph r i gi i 2 x2 − 2y − 1 + 3 y3 − 14 = x − 2  x3 + 7y = (x + y)2 + x2 y + 7x + 4 ma 9. th y2 +4 t 2 vào 1 t o đư c nhân t . 3x2 + y2 + 8y + 4 = 8x  x3 − y3 = 35 10. (1) – 3(2) Đ/s:(3; -2), (2; -3) 2x2 + 3y2 = 4x − 9y  4x2 + y4 − 4xy3 = 0 11. (1) – (2) Đ/s: (1/2; 1), (-1/2; -1) 4x2 + 2y2 − 4xy = 1  x3 + y3 = 9 12. (1)-3(2) x2 + 2y2 = x + 4y  x3 + 7y = (x + y)2 + x2 y + 7x + 4 13. l y4=4 3x2 + y2 + 8y + 4 = 8x 1
 x2 + 2y2 − 3x + 2xy = 0 14. xy (x + y) + (x − 1)2 = 3y (1 − y)  x2 + 2y2 = xy + 2y 15. nhân pt1 v i –y r i c ng v i pt2. Đ/s: (0;0), (1; 1) 2x3 + 3xy2 = 2y2 + 3x2 y vn  x2 + y2 = 1  16. 5 Hư ng d n: phương trình 1 nhân v i 25, phương trình 2 nhân v i 4x2 + 3x − 57 = −y (3x + 1)  25 50 r i c ng theo v .  x3 + 3xy2 = −49 17. l y phương trình 1 c ng phương trình 2 nhân v i 3. Đ/s: x2 − 8xy + y2 = 8y − 17x  6x2 y + 2y3 + 35 = 0 18. l y phương trình 1 c ng phương trình 2 nhân v i 3 5x2 + 5y2 + 2xy + 5x + 13y = 0 th.  (x − 1)2 + 6 (x − 1) y + 4y2 = 20 19. th ho c đ t n ph x2 + (2y + 1)2 = 2  x2 + xy + y2 = 3 20. c ng theo v 2 pt đư c (2x+y-3)(x+y-2)=0 x2 + 2xy − 7x − 5y + 9 = 0  x2 + 2y2 + 2x + 8y + 6 = 0 1 1 21. n ph x + 1 = a, y + 2 = b Đ/s: (0; 3), (-2; 1), −1 ± √ ; −2 ± √ x2 + xy + y + 4x + 1 = 0 6 6  x2 + y2 = xy + x + y 22. n ph x + y = a, x – y = b Đ/s: (2; 1) x2 − y2 = 3 ma  x3 + 2y2 − 4y + 3 = 0 23. đánh giá x. Đ/s: (- 1; 1) x2 + x2 y2 − 2y = 0  1 + x2 y2 = 19x2 24. chia r i đ t xy2 + y = −6x2  x3 − 8x = y3 + 2y 25. t o đ ng b c x2 − 3 = 3 y2 + 1  x3 + y3 = 91 26. (1) – 3(2) 4x2 + 3y2 = 16x + 9y  x2 + y2 + xy + 1 = 4y x2 + 1 27. n ph x + y = a, =b y(x + y)2 = 2x2 + 7y + 2 y 2
 (x − y)2 = 1 − x2 y2 28. n ph x – y = a, xy = b. Đ/s: (1; 0), (0; -1), (1; 1), (-1; -1) x (xy + y + 1) = y (xy + 1) + 1  x4 + 2x3 y + x2 y2 = 2x + 9 29. th x2 + 2xy = 6x + 6 vn  x4 − 4x2 + y2 − 6y + 9 = 0 30. l y (1) + 2(2) x2 y + x2 + 2y − 22 = 0  2y x2 − y2 = 3x 31. x x2 + y2 = 10y x√x − y√y = 8√x + 2√y  32. (9; 1) x − 3y = 6  (x − y) x2 + y2 = 13 33. 34.  th. (x + y) x2 − y2 = 25 xy + x + y = x2 − 2y2 x√2y − y√x − 1 = 2x − 2y  √  1 √ + y = 2 x + 2 35. x x y pt 1 thoát  √ 2 y x + 1 − 1 = 3 (x2 + 1)  2x (y + 1) − 2y (y − 1) = 3  36. 4+y pt 2 thoát  x2 + y − x = 2 x2 + y  √ 2 + 6y = x − x − 2y  ma 37. y phương trình đ u gi i đư c (12; - 2), (8/3; 4/3) √ x + x − 2y = x + 3y − 2   (xy + 1)3 = 2y3 (9 − 5xy) 38. nghi m (1; 1) gi i b ng phép th xy (5y − 1) = 1 + 3y x2 + y2 + 2xy = 1  39. x+y √ x + y = x2 − y x + √y − 1 = 6  40. . Đ/s: (3; 10), (2; 17)  x2 + 2x + y + 2x√y − 1 + 2√y − 1 = 29  12y = 3 + x − 2√4y − x  41. √ x  y + 3 + y = x2 − x − 3 3
 x2 − 4x = (xy + 2y + 4) (4x + 2) 42. . Th là xong. Đ/s: x = - 0.8; y = - 6 x2 + x − 2 = y(2x + 1)2  x2 + y2 + 1 = 2x + 2y 43. c ng theo v (2x − y − 2) y = 1 vn  x2 (y + 1) (x + y + 1) = 3x2 − 4x + 1 44. xy + x + 1 = x2  (x + y + 1) (x + 2y + 1) = 12 45. x2 + 2y + (x + 1) (3y + 1) = 11 √x + y − √x − y = 2  46.  x2 + y2 + x2 − y2 = 4 √  2x + √2y = 4 47. √ 48.  2x + 5 + √2y + 2 = 6  x + √y +   y + √x − th. √ x− y = 2 √ y− x = 1 bình phương 2√2x + 3y + √5 − x − y = 7  49. 3√5 − x − y − √2x + y − 3 = 1 √  x2 + 2 + y2 + 3 + x + y = 5 50. √ chú ý liên h p  x2 + 2 + y2 + 3 − x − y = 2  2y3 + 3xy3 = 8 ma 51. đ t t = 2/y. Đ/s: ( - 1; - 2), (2; 1) x3 y − 2y = 6  x2 + 1 + y2 + xy = 4y 52. th x + y − 2 = y x2 + 1 √8y − x + x = 2  53. √  3y − x + x + y = 2  1 1   3 + =2 54. (x + y + 1) (x − y + 1)3  2 x + 2x = y2   x2 + 6y = y + 3 55. √  x + y + √x − y = 4 4
 x2 + y4 + xy = 2xy2 + 7 56. −x2 y + 4xy + xy3 + 11(x − y2 ) = 28  x + y + x3 y + xy2 + xy = − 5  2 57. 4 x4 + y2 + xy(1 + 2x) = − 5 vn  4 x + y + √x − y = 8  58. y√x − y = 2 x2 y2  1 + =   2 2 2 59. (y + 1) (x + 1)  3xy = x + y + 1  x3 − y3 = 7(x − y) 60. x2 + y2 = x + y + 2 61. 62.  x + √ 2xy   y +    3 2 3 x − 2x + 9 y 2xy th. 2 − 2y + 9 x2 y2 − 8x + y2 = 0 = x2 + y = y2 + x đánh giá y 2x2 − 4x + 10 + y3 = 0  x x4 + y4 = y6 1 + y4 63. √ . Đ/s: (4; 2), (4; - 2)  x + 5 + y2 − 3 = 4  x + y + x2 − y2 = 2 64. . Đ/s: (-5; 3), (-5; 4) y x2 − y2 = 12 ma √11x − y − √y − x = 1  65. 7√y − x + 6y − 26x = 3  x2 + y3 = 2y2 66. x + y3 = 2y x√x − y√y = 8√x + 2√y  67. th là xong x − 3y = 6  x2 − 2xy + x + y = 0 68. th là xong x4 − 4x2 y + 3x2 + y2 = 0 √  x2 + x + 2 − √x + y = y 69. √  x+y = x−y+1 5
√x + y + √x + 3 = y − 3  70. √ x  x + y + √x = x + 3 √  x2 + 91 = √y − 2 + y2 71.  y2 + 91 = √x − 2 + x2 vn √  x2 + 2 + x + y2 + 3 + y = 5 72. √  x2 + 2 − x + y2 + 3 − y = 2  x4 − y4 = 240 73. x3 − 2y3 = 3 x2 − 4y2 − 4 (x − 8y)  y x + 1 = x − 1  2 74. x y (x − y) = x2 − 1  x2 th. 2√x + 3y + 2 − 3√y = √x + 2  75. (pt 1 gi i đư c) y3 + y2 − 3y − 5 = 3x − 3√x + 2 3 2(2x + 1)3 + 2x + 1 = (2y − 3) √y − 2  76. √  4x + 2 + √2y + 4 = 6  2 x3 + 2x − y − 1 = x2 (y + 1) 77. . Đ/s: (0; - 1) y3 + 4x + 1 + ln y2 + 2x = 0  2 2x2 − y2 = y2 − 2x2 + 3 78. . Đ/s: (0; 0), (1; 1), (-1;-1) x3 − 2y3 = y − 2x √ ma x2 + y + x2 + 3 x = y − 3 79. √ . Đ/s: (1; 8) x2 + y + x = x + 3 (8x − 3) √2x − 1 − y − 4y3 = 0  80. 4x2 − 8x + 2y3 + y2 − 2y + 3 = 0  2x2 − x (y − 1) + y2 = 3y 81. . T o đ ng b c x2 + xy − 3y2 = x − 2y 6