Tài liệu 392 bài tập hệ phương trình có gợi ý, đáp án từng dạng bài tập

DẠNG 1: PHƯƠNG PHÁP RÚT – THẾ 1) x2 y 2(x 2 xy x y) y 2) xy 2 y y x2 2xy y x4 4x 2 y x 2 (x 2 xy2 2xy 2 y HD : PT(2) 5) x(2x x2 HD : PT(2) PT(1) (x x2 xy 6) y x y 5 xy x y xy 2 xy x x HD : PT(1) 1 y4 ; PT(1) 2 2 3y2 x x x 2) 1 y x 5 2 5 5 2 2 5 2 ) ; 5 1 1 2 29 1 ; 29 2 (1) (1;2),(2;1) (y2 3y 2)(y 2 6y 11) 0 (1) 1 ; PT(2) 1 (y2 y(x 4 3) y)(y2 4y ( 1; 0),(0;1) 5) 0 (1) (1; 0),( 1; 2) (2) 1)(x y 4) 0 (1) 2 ( 1; (2) 3y 1 ; PT(2) y 1 (y 2 2y 1)( 2y -1- (1 2 y 1) 0 ) ) 0 3y 2y 2 1 ( (2) y2 1 ; (2) 1 (x ( 0 5 (1; 3),(2;1) 2 1) 2y 1 5 (1) 1 3x(y xy (2) y ; PT(1) 1 y y 5; ( (2) y ( 3 2) 0 (1) 8 5 y x x 2) 9 x 2 2 ;1 (0; 0),(1;2),(2;2) 14 x HD : PT(1) 9) 5y 2y y2 y2 x y2 7)( x HD : PT(1) 8) 0 9 ( 3 (2) 0 x x2 x2 1 3y 2 HD : PT(2) 7) 5y 3y 0 0 0 5y 1) 3 2 ;1 (1) x 3y)(x x 1) 0 y2 x 21) 1 x2 x 2x 1 3x 2)(4x 2 y x2 y x 6y (2) 3y y 2y 1)(y2 2)(3y 2 (1) 0 3x 2 HD : PT(1) 4) 1 (1;2),( 4 (y 0 y2 (y2 PT(2) 3x 3y x 3) y ; PT(1) 1 2y2 HD : PT(2) PT(1) (2) 5 y x 2xy (1) 5 HD : PT(2) x2 8 1 ),(2;1) 2 2 ;1 2) ) 2 2) TRƯỜNG THPT HAI BÀ TRƯNG 10) x2 x y2 xy y x x y 3(x x 3 y xy y x x 3 ; PT(2) 1 2x 3y 3x 2 y2 x2 x y x2 2y2 HD : PT(1) x3 x 2 x2 y 2 x 2 y 1 x2 y 2 2xy 0 (0; 3),(3; 0) 2 3x)(x 0 2 5x 8) 0 (2) (3y 2 8y 4)(y 1) 5 3 2 (2;1),( ;2),( ; ) 2 2 3 0 (1;1),( 23y2 ; PT(2) y ; PT(2) 1 2 0 (2) 1; PT(2) 9x 2 2xy 0 0 2y)(y 2 3y 5) 0 x (1;1);( 7x 2 x y 1 (1) 3; PT(1) (x 2 x)(x 2 x 6) 0 (0; 3);( 1; 5) (1) 1 (2) y 12 ) (45x 2 3 36x) 3 4 4 ; 5 ( 6x 2 x 1 3x 1 2y 2 13 ; ) 9 9 0 (2) 2 x 2x 59 31 59 ; ) 23 23 (2; 0),(0;2) (y2 3 2x 82y (1) 2y y (3;2),( 7 ; 3) (1) 2x y y2 6) (2) 3x x (x y (1) 0 HD : C1 : PT(1) PT(2) xy 2 4 y)x 2 y2 3y y2 3xy 21)(y (2) 2 (6 6x 2 4y 0 4 5 y HD : PT(2) (2; 3),( 3; 7) 2 (1) x 2x 1 (x 3y 1 ; PT(2) y 2y xy 2 (2) 5 xy (y 6 10y x ( 3;1),(1; 3) 0 (1) 3y 4x HD : PT(2) 19) y ; PT(2) 1 x xy 9 (2) y2 15) 18) 28 x2 HD : PT(1) 17) y) 11 y 13) 6y (1) y HD : PT(1) 16) 11 x 13) (CD 3y 2 2; PT(1) xy HD : PT(1) 14) y xy 2 HD : PT(1) 12) (2) x y 2 (1) 2 HD : PT(2) 11) 13 3 );(0;1) 5 0 (1) (2) ( 3 4 3 3 5 3 ; ) 3 3 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” -2- HD : PT(2) (3y2 PT(2) 20) 3x 3 x x y)x 2 (5 2 x C1 : PT(2) 4 y x2 21) (B x 2x y x4 2x 3 y x 2 y2 x 2xy xy)2 0 3) 2)(3x 2 0 (1) 2x 0 1) 6x 0 2x 9 (1) 6 (2) ( 4; 9 (x 2 4x)(x 2 8x 16) 0 6x 6 x xy 2 2 x 6x 6 C2 : (2) y ;(1) (x 2 4x)(x 2 8x 16) 2x xy x 1 7y (1) 22) (B 09) 2 2 2 xy xy 1 13y (2) C1 : x2 2 7y 1 HD : PT(1) x y 1 2 PT(2) (3y 4y 1)(12y2 23) x2 2xy xy y2 24) 1 3x 2 3x y 2xy 4 2 x y 5x HD : PT(1) y 26) 3x 3 x y x C1 : PT(2) PT(2) (x2 C2 : PT(1) y y2 )x 2 y y 2 2 0 2x)( x 2 x(x (2) 2)(3x 2 2 ;1 ( 3 5; 2) 1 5 2 (0; 0);(1;1) 0 0 (2) 2) (0; 0),(2;2),(1;2) 0 0 (1) 3 x ( 3 (1) 2 2xy2 2 1 (1; );(3;1) 3 0 0 2 0 (1) 2 x2 x 2x 1 1)(x 2 3x (6 2 (2) 3x 1 x 4) y 3x x 2 (2x 2 PT(2) (1) 0 2 x 4x y 0 17 ) 4 0 2 x HD : PT(1) y x PT(2) x 2 (x 1)2 (x 2 25) 1) 0 2 x2 5y 3y 1 y 2 1)(y y 1) 2y xy 4 3x y x (y2 x2 x 2y2 3y HD : PT(2) PT(1) (0; 4);( 2; 10) 4 x(x 08) (x 2 2x 2) (2) 2x)(x 2 C2 : PT(1) 2y 2xy y (x 2 PT(1) y2 4 2y 2 6y 22)( y2 (2) x 3 4x y2 ) 3) 0 0 -3- HPTVN ) TRƯỜNG THPT HAI BÀ TRƯNG 27) x2 2xy 2y 15 2x 2xy y2 5 28) xy x 2 2y 16 2 2x 4y x2 xy 2 y) yx 2x 2 y C2 : PT(1) y y2 HD : PT(2) 32) x 33) x2 x 2x HD : PT(2) y 34) (2x 2x 2 y 7y HD : PT(2) PT(1) (2x 2 15y 0 0 (1) 7 x ; PT(2) 1 y(2x 4)(4x 8y 32) 0 4x 2 (1;1) 2 (x 1) ( x 2) 1) 2) 0 ( 4) (1) (2) 6 9x 20 6 7 37 ; 26 2 7 9 ) 0 9y 9x 7 2)(2x 2 x (2) 9x 2x 2 2 (1) 2 x2 x 2 (2x 1)2 1)(37x 2 40x 3x 1)2 (5y2 (y (2) 2y y ( 4; 1) (2) 10 ; PT(1) 2 3 ) 2 (1) 3 x 2x 2 (1;1);(2; (1) 3 3xy 6 2y (1;2);( 2;5) 2 10 2y2 y (xy 2 PT(1) 3 2 x xy 3 0 1) y) y 4 2 3) 0 5 1 0 (2) x2 3 x y ; PT(2) 2x 2 6x 4 0 x x2 x 3 ; PT(2) 2x 2 6x 4 0 x xy2 HD : PT(1) y 5) y xy x2 y 3; 2 (2) 4y 2y)x y x y 2 y2 2(x 2y) 55) y)2 (x x y(x ( 3 (1) 7y 2 3)(x 09) x2 3 2) 0 (2) 4y 1 (2y C1 : PT(1) 31) 33 2 x(x 30) (D 2 2 ;1 (1) 1 x2 HD : PT(1) y(x 35) 2y 16 y 3 4y 1)(y2 14y y2 y(x 6x (1 x (y2 PT(2) (2) 3x HD : PT(1) 29) 0 (x 2 y PT(2) (1) x 2 15 y 2x 2 2x 7)( 3x 2 HD : PT(1) PT(2) 0 27) 1 1 16 ( ; );( 2; ) 2 7 7 9 3 33 ( ; 3) 4 0 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” -4- 35) x2 x x4 4xy2 y 5xy (1) 4y2 12x 2 y2 (2) x2 x HD : PT(1) y 5x 1 PT(2) x 2 (x 2 3x 2)(13x 2 36) xy x y x3 4x 2 37) xy x 2 y2 3y 2xy HD : PT(1) 38) x3 3x PT(1) 2x y y 39) 2x 3 y(x 4 6 5x 4x (2) y 40) x 2x)(3x 2 5x HD : PT(2) PT(1) 41) (x2 3x 12x 3xy y2 y2 2xy 5 (2x2 y)(x x(4x 1) HD :PT(2) PT(1) (x 2 y) 8) 1 x 2 1)(7x 2 (x 12x 8) 14x 22) (1; 3),( 3;15) ( 1 9 2x 6) 7;6 3 7) 0 (1) 5 (2; 1),( 2;1) (y2 ; PT(1) x(2x 1) 7 1)(y 2 2y 25) (2) 2 x 7 3 1)( 8x 2 4x 28) 0 (1) 3y 4x 0 0 (2) 2 2 23 153 44 23 ; ) 7 49 1 1 (0; 0),(1;1),( ; ) 2 2 (1) 11 6 (1) (2) 5x y) y ) (1;2) ( 0 2y 7 4 0 0 18 3)( x 2 y x 4) (2) x2 x2 6y 2 2 9 2x 2) (6y 2 (2) 2x y HD : PT(2) 42) y 17 (1) 2x 3 4x 2 HD : PT (1) y x 1 3 1 4 2 PT(2) x (x x )( 4x 2 2 2 (x2 17 1 ; (1;2) 2 (y x3 7 ; PT(2) 2x 5 1) 4x 2 y 2 2) (1) 3 2 2; 0 3y2 3 ( (2) 7 1)(7x C2 : PT(1) 4) 3y 2 ; PT(2) y 2 5y (x y 1 ( 2 1 x 4 x C1 : PT(2) 5y2 2 2xy 2 2y 3 18 x x 2)2 (x 2 2x 0 (1) y (x 2 PT(2) 2) 2 x HD : PT(1) 9x 2 1 (0; 0),(2; ),(1; ) 3 2 0 -5- 1 ( 4 17 3 ; 17 4 ) TRƯỜNG THPT HAI BÀ TRƯNG 43) x3 7y 3x2 y2 8y HD : PT(2) PT(1) 44) 4 (x xy 2x y y2 5) 45) xy 2 2 x y (1) y(x 2 1) 12y 46) xy 2 xy x 10y HD : PT(1) 47) x2 xy (x y)(4 x 2 PT(1) x 1 x2 HD : PT(2) y 1 50) 16x2 y2 4xy 17y2 2x HD : PT(2) 51) x2 x 7y 4 2) (x y)(4 xy) ; PT(4) x(y 4y2 20 16 2) 9y(x 3(x 2 y) (3) 32 (4) (0; 8),(2;2),(2; 6) 0 (1) (2) 1 (y 3x 2 1) ( 1; 1) 4y 1)2 (36y 2 4x 1 60y 80) 0 (1) (2) x2 1 x ; PT(1) 2x(x 1 (1) 1 (2) 7y 1 2y 1 5y 1)(32y2 3xy 0 0 1)2 (x y) 5x 9y 0 2 1) (1; 1),( 2; 2) 5 ) 2 0 1 1 (1;1),( ; ) 4 4 2x (4y2 PT(2) 2 1) y)(x 9 ; PT(2) 1 y xy x 2) (3; 1),(1; 1 / 3) 2 1)(x 49) 16 4y2 5y 3y 2;1) ( 2; 1) y)(x (x 16 1)y 1) 6y 32 y x2 x2 (y (2) xy) (2y x 1 2 1 (0; ),( 3 0 (x (1) 6(x HD : PT(2) xy; PT(2) 2y x (2) (2) 1 2x 1)2 (x 1) 0 7y 1 y 1 4y 1)(13y2 x HD : PT(3) 48) 2 (3y2 PT(2) 1 1 7y 2 5y 1 (1) 2y y2 HD : PT(1) 2 0 2x (3; 1),(3; 7) 8y. 2 2 1 (1) 0 6y 2 HD : PT(1) x2 y 1 PT(2) (3y2 4y 1)(12y2 y2 4 (2) 3x 2 3)(x 6y 2 7x 8x 8x 1) 2 x2 y 4 y)(x x2 (y 4 y)2 (x 0 (1) 0 (2) 1 (0; 0),(1; ) 3 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” -6- x2 HD : HPT 52) x2 (x2 y2 (2x 3y 3x 3y)2 1 2x y)y 1 3xy 3x2 y (3) 5x 2 0 2y (4) (1) 2y (2) (2;1) C1 :Rut the C2 :PT(1) 53) (2) 10x (x xy 30x 2 y xy 2)(x 2y) 2 2 (1) 2xy x y 1 10x 2 HD : PT(1) y x 1 2 PT(2) (15x 8x 1)(2x 2 54) x2 x 4xy 4 8x y HD : PT(1) 55) 3 4x y x2 (x 7x y(x 2 1 y 1 21 y2 PT(2) 3x 6y 2 2x y 2 (0; 0),(1;1),(2;1) 2)(4x 2 2) (1) 1 1) 0 (1) y 0 (0;1),( 1;2) (2) y); PT(2) (x y 1)2 0 (1) 10x (2) 4y 12) (5 2 2 ;2 2 (1) y(x 2 1) 6y 2 y 1 3 1 y )(36y2 4 3 12y 2 1 (2) 1 (0; ),( 3 15y 3) 0 (1) y 8 (2) y x2 2xy x4 4x2 y 8 x 3x; PT(1) y 3x2 2 2) 0 16 HD :PT(2) 0 1 (1; 1),( 1; 3),( ; 3) 3 (2) x2 (y2 x3y 2x 5y 2 x y 2 4y 4)( y2 1) 3x 5x 2x y(x 4y xy 1 2) x2 2 4x 2 (x 2 0 2 (y2 (2) x2 y y xy HD : PT(1) 60) 2 5y 4 0 1)(yx2 x2 x2 (y 2 1)2 2x PT(2) 59) x ; PT(2) 2 y) 0 (1) 2 2x 1)(x HD : PT(1) 58) 2 1) 1 1 1 (1; 4),( ; 0),( ;2),( ;1) 5 2 3 0 4y (x (2) 3x 2 x 4x (x HD : PT(1) 57) 3x 1)x 2 (xy 2y y HD : PT(1) 56) x 2 0 0 y2 (x 2 (2;2) 2) ( 3x 2 4x (1) 0 (2) -7- 4) 0 2 ;1) TRƯỜNG THPT HAI BÀ TRƯNG x2 x ; PT(2) 2x 1 y ; b 2y 1 x C1 :PT(1) C2 :a 61) x y2 4xy y4 8xy2 C1 :PT(1) C2 :a 62) y2 x HD :PT(2) (y2 x 9x HD : PT(2) 64) 10x 30x x PT(1) 67) x2 x 3 8y2 2xy HD : PT(1) 8xy 2 3) 3 13 2 3 17 2 ; ; 11 3 13 2 10 3 17 2 ) ) 0 2y (1) 1) (2) 2 ( 3; 1) ( 3x 49x 4 78 ; 13 78 ) 13 0 49 y 2 (1) 8y 17 (2) ( 1; 4) 49 24xy) 0 (x 2y)(x 2 (1) 12y 12 ;1 1 (1; 4),( ; 0) 5 49 12 2 (2) 1) 3xy2 2 x 2 0 1 5x x2 3 24) 1)(2x 2 (x 1) y 3(y x3 x ( ( 3x y3 3 y2 HD : PT(1) (1) 3 x xy 66) (HSG QG 2004) 3 (1) 2 x(x 2 PT(1) 1 0 1 8x 2 y2 HD : PT(2) ( 1; 1) 2 x3 0 (2) 2xy A06) 2) ( 4) 10x 2 HD : PT(1) y x 1 2 PT(2) (5x 6x 1)(6x 2 65) (DB 2)(4y2 2 3xy y xy y 9x 2 2)( x 2 2 3y (2) x2 3x xy 2 y2 (y2 3 y (x 2 PT(1) (0; 0),( 1;1),( 1;2) (1) y2 2)(4y2 2y (0; 0),(1;2),(2;2) 0 1 2y2 y)x 2 (9 2 4x 2y 2) 0 y2 y ; PT(2) 1 2y x 3x 3 3y2 1 2 y 2y2 2 x 2)(4x 2 3x 0 4x2 2x ;b y 2x 2 PT(1) 2x 2x y y 63) y x 2 (x 2 x 2 0 (2) 2 8y ; PT(2) (2; 1),( 2;1) xy 4y2 ) 0 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” -8- 68) x3 4y 1 2 y y3 5(1 HD : HP(2) x 3y2 3xy x y 2 y3 2 x y(x 1 3y 1 4x 3y The 4 3y 2 2 4x y 4x 2 2x x2 y 2 xy x2 y2 3 3 y x3 4x 4 y3 6y x 5y 3) 3 0 (1) (2) 3 ) y2 (1; 1) (3) 3) (1) 3 (2) (x 2y)(x 2 2 2xy 4y ) ( 2; 1) 0 (1) 2 (2) 2y 3 xy 2 2.7 (3) 2 (4) (2x y)(x ( 1; 2),(2;1) 2y)(x y) 0 xy 1 (1) x 3y (2) xy2 A06) 0 ( 1; 1) 2 3 4x 2y (y x)2 x2 ) (0; 0) 0 1 (1) (0;1),(1; 0),(1;1) y (2) ( HD :Thay(1) vao(2) 76) (DB yx y)(2xy y2 y4 x3 (4) HD :Thay(1) vao(2) 75) x 2y y) 2 y)(4xy2 1)(4x (x y) 2 x 4(2x 7 2x 3 xy 2 3 1 3 1 ; ),( ; ) 5 5 2 2 (1) HD :Thay(4) vao(3) 74) 2y 3 ( 3 y2 1 y3 xy(x HPT y2 ; PT(1) (2xy HD :The(2) vao(1) 73) (1) 0 (2x xy x3 x2 y3 ) 2 9y 3 0 (2) 5y) 2xy 4y) (2) 9y 3 9 y)(7x 0 3y vao PT(3) 16x 3 2x 3 y 2 2 x(3x 4 y)(x 2 0 2y 2(x 3 16x 3 y 3 (0; 2),(1; 3),( 1; 3) 4 20y 3 HD : PT(1) 72) 5x 2 y3 x3 71) 2 4x) 2 x (2) x) 4(y HD : PT(2) 70) (1) 2 x3 PT(1) 69) y 16x xy(x x3 8x x2 3 HD :Nhan cheo ve voi ve 2 4xy y3 3y2 2x(x 2 3y ) 0 3 3 25 ; 3 3 25 ) 2y (1) (3;1),( 3; 1) 3 (2) ( 3y)(x 4y) 0 -9- 4 78 ; 13 78 ) 13 TRƯỜNG THPT HAI BÀ TRƯNG 77) (DB B06) (x y)(x2 y2 ) 13 (1) (x y)(x2 y2 ) 25 (2) (3;2),( 2; 3) HD :Nhan cheo ve voi ve 78) (6 x)(x2 (3 2 y)(x y2 ) 6x 8y 2 8x 6y y) HD :Nhan cheo ve voi ve 79) 2y(x2 y2 ) x(x2 y2 ) (x (1) (0; 0),(2;1),(4;2) (2) 2 2 y )(x 2y)(4x 3x (1) 10y (2) 2y 15) 0 (0; 0),( 2, 1) HD : Nhan cheo ve theo ve 80) (DB 27x 3 y 3 D10) 9x2 y 27x 3 y 3 PT(1) 81) (DB 1)3 xy(5y 8 42xy 63x 2 y2 ( 2 1 ; 2),( ;1) 3 3 ( 1 1 ; 3),( ; 2 2 0 2 9x 9 (1) 0 (2) 3xy2 9x (3) 6x 2 y (4) 5xy) 3 ),(1; 3) 2 (1;1) (1) 3y (2) 1 3y 5y 1 1)( 375y2 1 ;b y xy 5) x 2 2y 3y x2 x y 1 y 2(x x2 135) 2y( x 2 3 0 2y) ( 6 3y; PT(1) 5 2 3) x 1 x2 HD :PT(1) y PT(2) 3)(x (x 50y 6 HD : PT(2) 84) 7y 3 xy x 2 y2 1 y 3 (y (x2 3y 6x 2 y 2y3 (9 1) C1 : PT(2) C2 :a y 9x (xy x 6x y (2) 42xy 2 3 15 ) 2 (1) 42xy 6xy 2 4x 3 y2 HD :HPT 83) 4x y B10) PT(1) 7y 3 2 8 6x 63x 2 y2 2 82) y2 63x 2 y2 HD :PT(2) 7y 3 5 15 , 2 ( 5x 2) (1 5y) 6 3 4 21 4 2(x 5y 5y 9 (3; 3) x 1 3 ;1) 3 ) 4 0 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” - 10 - x 85) x y2 x y y 2y 4 4 3x 6 x2 xy x (x 1)2 3(y 2 2 x 88) 1 x( y 89) x2 y 90) x2 91) 1) 2 6xy 0 6y(y 1) 7 y 1 1 1 x 5x xy 3 1 x2 y2 2 x 2 y2 x2 5 2y 3 y 3 x4 x3 1 HD : PT(2) x y y(2x2 0 (2) x) 12 (2) (1; 12) 2) 9 ),(3; 0) 8 0 (3; 3),( xy 2 y2 y) 14 2 3) (0; 3),( 2;1),( 4; 1) (y 3)( 2y 2 1) ; PT(1) 3; 0 y2 ; PT(2) x 1 2 y2 y) 0 (1) (2) (x 2 ;2 (1) y y (1;1),(2 0 (2) 3 y (2) ( 1; 3) 4 y2 xy xy2 0 (1) x2 y 2y) 1 x2 y2 y2 x (1) 13y 4x 3 4 0 1 (x 2 xy2 x 2 3x 1 2 (2; 1) 0 y2 y HD : PT(1) 92) x x 1 7 3)(x 2 x2 HPT x2 1 2x 2 HD : PT(1) PT(2) y 0 x y 6 x2y 3y2 1 (1) 3 y 6y2 HD : PT(1) 1 x x2 3y 2y y (1) x 2 0 (2) 2(xy 2. 1)( x 2 x2 2 y x 1) y x2 (y x)2 0 xy 3. (3 2 4 x 3 x)2 (y 0 3x x PT(2) 2) 1 PT(1) (4;2) ; PT(2) y y HD : PT(1) 2 2x A05) 0 2 5y 2)( y2 HD : PT(2) 87) y2 x x y 86) (DB 1 2y x HD : PT(1) (y2 1 (6x 2 5x (1; 0) 1) - 11 - 0 TRƯỜNG THPT HAI BÀ TRƯNG x 3 93) (B 02) x HD : PT(1) 94) y x y 3 x y x y 6x 2 3x y 98) 2 y)3 (x (x y2 2 (2) 1) 3(x y 2y 1)(3x x x3 ) 1) y 1) 0 3 1)3 6x(x 1)2 3y(x (1) y x 1 y x (2) 1 HD : PT(1) 100) (A y y 4x 14) HD : PT(1) (x (y x 12 x3 x 1 1 0; PT(2) y2 ) y 1 (0;1),( ; 0) 3 (2) x(y 2 4y 3 4y x x3 0 1) y2 y y) y 8x 1 12 y 0 (2) (y 1) 14 5 ; ) 9 18 0 2 1) (y 2 3) 4 3; 3) 0 (1) (2) y2 ) ( (0; 1),(7 2)2 3 1)(x (2 3 4 ; 3 4) (1) 1 y)(x x 2 2x (x y)2 (1 0 1)2 3y(x x 0 0 3) x y 2y 2(x y) (1) (x 2y)(x 3 x 2y y) (x y)2 (1 (2) 3x (y HD : PT(1) 99) (x (1) xy HD : PT(2) y)3 1 2y2 2(2y 3 (2) y x2 x2 2 x (2x 3 1 (1;1),( ; ) 2 2 (1) (1) y)2 3xy y (x x HD : PT(2) 97) y)2 (x y x 3 HD : PT(1) 96) x y (x HD : PT(1) 95) y (2;1) 0 y(12 x2 ) 2 y 2 12 (1) (2) (3; 3) “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” - 12 - DẠNG 2: PHƯƠNG PHÁP CỘNG 101) x2 3x y2 2 2y HD : 3.(1) 102) 5x 16x (3x 2x 4y y 1.(2) x2 x 2 2xy (2) 7x x 1 1)2 x2 (2y x2 (2x 9 y 5) 2) 3 (1) 3)(2x 1 y2 2x y 1)y 1)2 2 ( 2) 5 3 2) 6y 3x 2) 2)(2x 13)(x 2y 2 3) 0 (1) 1) 3y 13 (1) 3y2 2xy 2x 11 (2) 9y 4x2 3y(x 1) 7 (1) 3y2 4x(y 1) 3 (2) HD : 8.(1) 3.(2) 3y 5)(2x 2y 13)(4x 3y x2 2 x(y 1) (1) y2 7 y(x 1) (2) 2y 4)(x y ( 3;1);(0; 2) 0 3xy (8x ( 1; 1) 0 (2) 2y 11 12 ; ) 5 5 (1) 0 y (8x ( 1; 0);( 0 20 3y 1 ;1);( 1; 0) 2 (2) y 4y2 2y (x 3 2 ;3 0 (2) (3x 4xy y (1) 3)(2x 2y2 2.(2) (2 0 (2; 1);(1;1) 2x2 HD : 1.(1) 0 28 24 ; ) 29 29 0 9.(2) 111) ( 4) HD : 8.(1) 110) (2) (2) y 2xy (x y 0 2y 6(x y2 HD :PT(1) 5y y 4xy 13 (1) (2x 2x2 3 ; 0) (1) (2) 4.(2) (x 13)(x 2x xy (2) y y y2 2 (2) 3)(x 2xy 0 6y 33 y 2y2 16 8)(x (2x 1)2 3x2 8y 13 ; 4) 2 (4; 0);(0; 4) 0 3 (2x x2 ( 3 (1) (x y2 xy ( (2) 2y 16 1.(2) 109) 4xy 2y HD : 2.(1) 108) x) 2 HD :(1) 107) 4)(4 3x x 3 20y 2 HD : 1.(1) 106) 2 (1) 8y xy HD :(1) 105) 1 5y2 5.(2) HD : 2.(1) 104) 9x (4x 2 HD : 7.(1) 103) 4y 1.(2) y2 y 3x 2 3) 1) 5) 7 ( 4; 3);( 2; ) 3 17 ( ; 7) 2 0 0 5 (1; 2);(1; ) 4 19 (4; ) 3 ( 0 - 13 - 1 ; 2 7 ) 2 TRƯỜNG THPT HAI BÀ TRƯNG 112) x2 2xy xy 2 HD : 1.(1) y 2y2 3x 3y .(2) 1 0 (1) 0 (x (2) 2y 1)(x 2y 2) 0 1 5 113) (HSG Nghe An) 57 2 4x 3x y(3x 1) 25 HD :25.(1) 50.(2) (15x 5y 7)(15x 5y 17) x2 114) 2x 2 x2 y2 3xy HD : 8.(1) 9x 2y2 xy y2 3x 15.(2) (x 6y 6 12y 10 2y 0 6)(x y2 xy (1) (2) 11y x 33) 7y 115) (HSG Dien Bien) x x 12 y HD : 4.(1) 1.(2) (x 4y)(x y 116) 2xy 3y2 2x 10y y2 2y 0 2x2 2xy HD : 2.(1) 9.(2) (8x y2 xy 2y x 2y 2 0 (x y 117) x2 2x 2 y 2 HD : 1.(1) 3.(2) 118) (DB A05) HD : 1.(1) 2.(2) 119) 2x2 2y 2 y2 8 2 120) x 2xy HD : 1.(1) 1.(2) 121) x2 y2 x2 2xy 2x2 x(y 122) x2 HD :3.(1) xy 4.(2) y 2x 4) 1) 0 ( 2; 4),( 2;2) ( 12 3 ; ),(3;1) 5 5 (0; 0),( 2; 4) 0 1) 2 4 7 7 5 7 ; ) 7 7 (1) (1; 2),( 2;1) (2) ( 2; 2) (1;2) 3y 2x 3 17 0 5) 5 2)(y 2 1 11 2 ( ; ),( ; ) 5 5 25 25 ( 0 4 1)(9x y (y 4y (2) 2x ) ( 7y 1 2 (2) (1) y 5 (1) y) 3 2xy y2 7x 1.(2) y)(x (3x xy HD :1.(1) y(y x 2y 3x 2 1) x 7.(2) 2y2 y 1 3 17 34 8 17 ; ) 17 17 ( 1; 2),(1; 0) 1)(5x y 5; 2) 0 (1) 2)(2x x (x 4) 0 y2 x(x 3y HD : 17.(1) x2 x2 (2) 2 ( 3 (1) (2) 3y (2) 2 2 ;1 0 2 x2 (1) ( 3 0 (1) ( 1; 0) (2) ( 3) 0 11 12 ; ) 5 5 (1) 5y (y 9 2x 3)(y 1) y2 3y2 x 2y (10x 9y (1;1);(2; 1) (2) x 2) 0 3y (1) (2) 1)(x y) (0; 0)(1;1)( 1;1)( 0 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” 7 3 ; ) 43 43 - 14 - 123) (DB C1 : 3.(1) C2 : PT(1) 124) y) (1) x2 xy y2 7(x y)2 (2) (x y y)2 x4 2x2 y x2 y2 (x 2 4x 2 y2 2 2 2y x2 x 2 xy y2 xy 2 y 2x2 y2 9 22 0 2xy 9(x y y y)(x 0 3) y 1) 0 0 (1) (2) 2 4y y 27) 5) 0 y)2 2 ;5) (1) (2) y) (x y)2 21(x y) 0 5 ( 2; 3),( 0 y) 7(x 5x 1.(2) 0 7)(x 7(x y)2 xy C1 : 1.(1) 6y 19(x xy 21(x y) 2)(x 2 y (x y 22 2y x2 y 1 8y 15)(y2 HD : PT(2) PT(1) y) 2 2.(2) (y2 PT(1) 3(x (0; 0),(1;2),( 2; 1) 0 3 x4 x y)2 y) 3 (2) xy 1)(x 9(x y C2 : PT(2) 127) 3(x (x 9(x C1 : 1.(1) 126) y2 xy HD : PT(1) 125) xy D06) 1.(2) PT(2) x2 (0; 0),( 2; 3),(3;2) 21(x y)(x y 1) 0 (1) 7 (2) (2x y ( 1; 3),(1;1) 1)(x y 2) 0 C2 : Rut the 128) x4 4x2 x2 y C1 : 1.(1) 2x2 129) 5x 2 3x 2xy 2y 2xy 5y2 x4 1.(1) y2 2 xy 2x C2 : 1.(1) (2) 12)(x 2 y 4) 0 (y2 17) 3x 2y 0 (1) (1; 0),(0;1) 3x 3y 2 (2) 4 6 5 ( ; ),( ; 7 7 7 3 ) 7 ( 3;2),( 3 ; 8) (2x 8x2 6y y 38 y 2)(2x 1 0 y 1) 0 (1) (2) 38 y y 2 10y 16)(y2 2.(2) (x 2 ( 1; 3),(1; 3) 8y x2 C1 : PT(2) PT(1) 2 (1) 23 2 HD : 3.(1) 130) 6y 2 (x 2 y 23 6y x2 y 2 8y 15)(y2 (y2 2 4y 2.(2) C2 : PT(2) PT(1) y2 y 8y 11)(x 52) 2 y 0 7) 0 - 15 - TRƯỜNG THPT HAI BÀ TRƯNG 131) x4 2x2 y x2 y2 C1 : 1.(1) y x2 y y3 2y x (2) y 3) 0 y2 y (2) (x 2 y)(x x2 y 03) y xy 3) (0; 0) 0 2 (1) (1;1) 2 (2) x2 y)(3xy (x 2 2 y2 3y HD : (1) (2) x2 3y 2 0 (1) y2 3x 2 0 (2) HD : (1) 134) x y y) 3) 0 (1;1),(2;2) (2) (x y)(x x 2 xy x 2y (1) y 2 xy y 2x (2) HD : (1) (2) (x y)(x 2x y 135) y 0 1) (1) x2 3 (1;1) 2y x HD : (1) (2) y2 (x 4 y2 (1) 4 2 (2) 137) x2 y xy 2 HD : (1) (2) 2x2 y 138) 2y 2 x x 3 3 (0; 0),( ; ) 2 2 0 3 136) (2) y)(2x 2 (x y)(x 1 y 1 x (x 2y 2 ) 3xy y xy) 0 (2;2) 0 (1) (1;1) (2) HD : (1) (2) x3 x2 x 1 2y (1) y3 y2 y 1 2x (2) 139) HD : (1) 140) (x y)(x y)(x y 2 xy 2xy) y 2 0 x y x3 2x y (1) 3 2y x (2) y HD : (1) 141) (2) (2) 3 ; 1) (1) 3x 133)(B 2)(x 2 y 3 2x ( 1;1),( (2) (x2 x3 HD : (1) (1) 3 1.(2) C2 : PT(2) 132) 3 (x y)(x2 y2 xy 1) 3) (1;1),( 1; 1) 0 (0; 0),( 1; 1),( 3; 3) 0 2x 3 4 y 4 (1) 2y 3 4 x 4 (2) (3; 3),( 11 11 ; ) 9 9 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” - 16 - 142) 143) x 1 y 7 4 (1) y 1 x 7 4 (2) x 1 y 2 3 (1) y 1 x 2 3 (2) x 3 2 y 3 (1) y 3 2 x 3 (2) 144) 145) 2x 3 y 3x2 y 3 6xy HD : 4.(1) 146) y3 2 2y HD : 1.(1) 147) 2x2 150) y3 x2 2y2 8x 3 y3 152) (x 4)3 4y 3)3 (y x y 5 (2) y)3 (3 x 0 7 y (2) 3 (x 1) 3 (y 2) x (1; 2),(2; 1) y 3 18y 3 (1) y2 (2) 18y 3 108xy 72x2 y2 108xy (x 1) y x) y 1 1.(2) (x 1 27 y 0 6 (1) 4 (2) y 1 2)(x y 1 (0; 3),(1; 0) 5) 0 x 1(1 2y) y 2 0 (1) (2;1) y(y x 1) x 4 0 (2) 19 ( ( x 1 y)(2 x y 0 HD : 3.(1) 153) 2)3 72x2 y2 (2 (2; 3),(3; 2) (1) 6x 1)2 3 (2) 9y 27 HD :1.(1) y 9y 16x x 8x 3 y 3 x x 9 HD : PT(2) 151) 2) (1; 2),(2; 1) (1) 3.(2) (x (y 91 x3 PT(1) 3 (1) 3.(2) 4x2 y (2) 1) (x 3y2 HD : 1.(1) 0 3 4x y3 4x2 3 35 3.(2) HD : 1.(1) 149) 4y (x 3y2 x3 y) 3 (1) x y3 HD : 1.(1) 148) (2x 3.(2) x3 (1;1),( 2; 2) (2) 3 9 2 (3; 3) (1) 7 1.(2) x3 x 5 2 (8; 8) 2.(2) 4x y 4 (1 HD : 4.(1) (8 1 3 1 x)(1 y) 6 1 1 2y 3) 0 (1) x 1 0 ( (2) 3.(2) x 2 1 y 3)(2 1 x 2 1 y 3) - 17 - 0 3 13 3 13 ; ) 8 4 3 ; 0) 4 TRƯỜNG THPT HAI BÀ TRƯNG 154) 155) x2 2 y2 3 x y 5 (1) x2 2 y2 3 x y 2 (2) x2 x y 1 x y2 x y 1 y 18 x2 x y 1 x y2 x y 1 y 2 (4; 4) DẠNG 3: PHÂN TÍCH THÀNH PHƯƠNG TRÌNH TÍCH 156) x2 3x 5x 3 xy HD :PT(1) PT(2) y 2 (x y 2 9 2xy 9 2x (1) x 6x 2 3)(x 2 18 (2) 5x 2 2x 6) (1; 3),(3; 15) ( 1 17 ; 4 7 7) 0 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” - 18 - 157) 2x2 y2 xy x2 y2 x HD : PT(1) 158) (CD y (y x HD : PT(2) C2 : PT(1) y PT(2) 1)(x 2 (x 2xy 3x 2 2 x 4y HD : PT(1) 161) x 6 2 HD : PT(1) 162) x2 y2 HD : PT(1) 163) (1;1),( 4x 12y 2x 4) 3) 0 2y 2 2)(y 3 3) 2y2 (2) 3x 3y 2y 2 (1) 0 (1) 4x(y 1) 3 (2) 1)(3y x2 2y2 2xy 2x 2 y2 2y2 x2 4x 3) 15 0 y x y 4 (2x y 1)(x 3x (x 2x2 xy 3x2 2xy (x 2y)(x y2 2y 5) 2 0 7y y) 3x 2) y)(2x y) 0 (1;1);( 0 ; 1 11 4 0 0 4 ; 5 ) 13 ) 5 (1) (1; 1);(3; 3) (2) ( 13 (1) 1 4 (1) 0 y 11 ( 1; 2),(1; 1) (1;2),(3;1) (2) 3 3 0 0 y ( 5 19 ( 2;1);( ;1),(4; ) 4 3 (1) 0 y2 0 (1; 3);( 2; 0) 0 0 y2 xy 1) (2) 3)(x 5x x2 2y 5 y2 xy HD : PT(1) 4y 2y xy x2 2)(2x (2) 7 8x 5) (0; 3),(2;1),(2; 3) 0 1) 4y2 ; 0 3y(x (x 2 (1) 4y x2 5 1 3 ( 2; );(2; ) 2 2 7 3 ( 2; );( 6; ) 2 2 3 2)(2y (y 1 0 2 3y 0 0 4x 2 HD : PT(1) 167) y y HD : PT(1) 166) 1) 2xy (x HD : PT(1) 165) y2 1)(2x 2 x 4xy HD : PT(2) 164) x 6 4xy 0 x (x 2x 2 (2;1),( 2; 1) (2; 3),( 3;2) 2y 1) y 4y 4y x x2 y)(2x 3x 2x 0 4 13 ; ) 5 5 0 x2 y (x xy y 2 (1;1),( 7 2y)(x 2 1) 2 2y 2x 3 (1) (2) y2 x 0 2x xy xy (x 2 160) 2)(y 2 C1 : PT(2) 2 0 xy (x 12) y 4 x x2 14) 159) (D 5x (2) - 19 - 157; 13 157 2 1 1 ( ; );(3; 3) 2 2 5 45 5 45 ( ; ) 10 5 ) TRƯỜNG THPT HAI BÀ TRƯNG 2x2 168) 2xy x2 (x 2x2 x 5xy HD : PT(1) x2 170) x 2x y x y y y 2 2x y 11) 3)(2x y 2 y 2 y2 2 4)(4 x) y2 5x2 4xy 16x 5x y 2 1) 0 2(x y) 2 (x y)2 y2 2) 0 8y 16 0 x 4) 0 4)(y 3y (x 4 ; 5 13 ) 5 2 ;1);(2; 3); 5 1 4 ( ; ) 6 3 (1; 1) 0 3y 3 1)(x2 (y 1) x 2x (5x (2) 0 1 ( y2 C1 :(1) 1) 4 y2 ) 2y y 2y xy(x2 xy 0 1 4xy2 x2 ( 1; 1) ( 5x2 y x (2) 8 (0;1);( 5; ) 3 (1;1);( x)(y y2 0 1 2)(2x xy xy 5) (1) 1) (1) (2) 0 2y y)(x (xy HD : PT(2) 0 4 2x x 15 3 (y HD : PT(2) 176) (x (x HD : PT (1) 175) y xy 0 5x x 2x2 y 3 174) (A 2 18y y y (2) 2 x 6x HD : PT (2) 173) 3x y)(x 2xy 2x 3 11x 2 2x y xy 2 0 3y xy y2 1) 2 HD : PT (1) 172) y)(2x (x 2 2 0 xy HD : PT (1) 171) 1 (x 3 (1) x 2y 2y2 3 0 3y2 7xy 2 y 3y2 5xy HD : PT(1) 169) x 0 17 2 ;10 17) (1;1);( 1; 1) ( 2 10 ; 5 10 ) 5 (0; 4),(4; 0),( 4 ; 0) 5 0 0 y)(x y 1) 4y 3 0 0 2 1 (0; 0),(1;1),( ; ) 3 3 C2 : Rut the 2x2 8xy2 xy 16x 3 2x 8y2 HD : PT(1) (x 177) 178) x2 5x 2 4x y HD : PT(1) 5 0 4y2 )(2x xy 3y y) 0 6 3xy 2y 2 9 (x 3)(x 2 1 ( ;1); 2 3 19 3 19 ( ; ) 4 2 3 233 ) 4 1 9 ( 1;1);( ; ) 4 4 ( 3; y) 0 45 “ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian” - 20 -