Toán 10- chuyên đề hàm số - 2b
www.tuhoc.edu.vn VD1: x2 4x y 2log2 (x 2) log y (x,y ) x y x y (I) = HD x2 4x x y (1) y (2) x2 – 4x + x = x2 – 3x = (x ; y) = (0 ; –2) (x ; y) = (3 ; 1) htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn VD2: x(x y 1) x2 y)2 (x (1) (x,y (2) ) = HD x x x2 3x x2 y x2 x x x x 2 y = y= 3 ) (2; (a) log (y x (c) x) log4 y x 3y (b) y)2 log2 (2x log (3y 2x) 4x 25 log2 (3y 1) x y 3y 16 x htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn VD3: xy x x2 y x 2y 2y y x (1) 2x 2y (2) = HD x y 0 x y (*) x2 – xy – 2y2 – (x + y) = (x + y)(x – 2y – 1) = x – 2y – = (do x + y x y 0) x = 2y + (2y 1) 2y y 2y 2y(y 1) y=2 2(y 1) 2(y 1) 2y (do y + 1> x2 y2 y 0) x=5 VD4: x (*) y x x y y ( x y 1)( x x y x y (1) (2) = HD y (I): (II): htttp://tuhoc.edu.vn/blog x y x x y y x 1 y x y x y x x vµ y 1) y y x y 1 1 1 , 4 www.tuhoc.edu.vn y2 y (a) x2 x2 x 3y (b) xy x 2x x 2y x2 y2 2xy y 5x 2y 4xy xy(x 3y3 y2 ) 2(x y) y)2 (x x y x x y x y x x htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn VD5: y2 (5x 5x y 4)(4 x) (1) 4xy 16x 8y 16 (2) = HD y2 – (4x + 8)y – 5x2 + 16x + 16 = ' 9x y 5x y x x y 4 x hc y x x y y 4 ;0 5 2x 2xy y2 xy 5x y 2 htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn VD6: x2 y x4 y2 x3y xy xy xy(1 2x) (1) (2) = HD x2 (x u x2 v xy y)2 y 1) xy u v uv y u2 v u3 u2 y ,v= xy u2 u x xy x2 (4) v u u2 u u v v v x2 (3) u2 u htttp://tuhoc.edu.vn/blog xy(x y y 3 2 vµ y = x = y = 25 16 www.tuhoc.edu.vn VD8: x2 (x y(y 1)(y x) 4y (1) x 2) y (2) = HD 0, chia hai x2 y y x2 y y x2 u y , v y x x x ta cã: u v uv x2 y x y (1 ; 2) (–2 ; 5) (a) xy 2 xy x 7y xy 13y (b) x2 3x y2 2y 3x 4y 9x 8y x y x xy y htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn TOPPER Chú ý VD9: f(x) = f(y) x=y x3 5x y3 5y (1) x8 y4 (2) = HD 1, y4 |x| |y| Ta có: f (t) 3t t [ 1; 1] suy x = y u + x4 – = y x x3 3x x2 y2 (4x 4x 9x 22 x y y3 3y 2 1)x (y 3) 2y y 9y 4x htttp://tuhoc.edu.vn/blog www.tuhoc.edu.vn x 1; 2 3; (1 ; 1), (–1 ; –1), (b) ; , 2 10 10 ; , 5 PT (1) x 1; ; 3; , , (1 ; 1) 10 10 ; , (1 ; 1), ( 1; 1) 5 y 1 ; , 2 (a) (3 ; 1), y x y x (y 3) x y x x ;1 (b) 13 ;0 , 13 ; (3 ; 3) ; 2 vµ ; 2 ;2 htttp://tuhoc.edu.vn/blog