Truy cập www.khongbocuoc.com để download thêm tài liệu học tập khác www.VNMATH.com PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH VÀ HỆ PHƯƠNG TRÌNH ( x + 1) x − x + = x + sin n x + sin 1+ x m +1 = cos n x + x − x − x2 = − x2 2 cos m+1 x với m , n số nguyên dương x − 3x = x + −1= oc c om 4x + + x x + 2006 x3 + 1006009 x + x − x + 2007 + 1004 =  x ( y + z )2 = ( 3x + x + 1) y z 6 x = y (1 + x )    6 y = z (1 + y )  y ( z + x ) = ( y + y + 1) z x   2 2 2 6 z = x (1 + z )  z ( x + y ) = ( z + z + 1) x y  cos 2x  3 + tan x = x + = x − x − 10 1 +   cos x  11 ( x − x )( x + x + 2007 ) − 2005 x − x = 30 x + x − + 2006 6 x x3 − x + = ( x + x − )( x + )  13  2 x + ≥ + x x  14 x3 − 3x + = 15 2005 − x bo cu  x + xy y + 2z = ( ) ( )   −3  2 12  x + y + xy + xz + yz =  x + y + z = x < < y , z  2006 + 2006 − x 17 x + y − z =  18  x + y − z = 37  x3 + y − z =   y − + x = 19   x + y = 82 kh on g 16 (16cos x + 3) = 2048cos x − 768 2005 =1 x + + = x3 + 3x + x 20 16 x − 16 x5 − 20 x + 20 x3 + x + x − = 21 11x − 14 x + + 11x − x + + 17 x + x + = ( x + ) 45 22 x + x + − x − x + 40 = x + x + 24 x − x − = x + 23 x − 11x + 21 − x − = x (4 − y2 ) = y  25  y ( − z ) = z 26   z ( − x ) = x 27 x + + x x + + ( x + 1) x + x + < Sưu tầm: Hồ Văn Diên – THPT Thái Lão  x + y + xy =  2 x + = y + x Truy cập www.khongbocuoc.com để download thêm tài liệu học tập khác − x2 + x −  y +1 x = + x   z +1 31  y = + y   x +1 z = +  z  13 13  y + x + 16 + x − y = x + x + 16  97  30  x + y = 36  x <  y > 32 x 2008 2007 + − 20082 − x = 2008 x 2007 > 2x om 28 x + www.VNMATH.com 29 x + 35 > x − 12 x ) ( 38 x + x + + ( x + ) ( ( + x + x + 1) = ) kh o  x + y − x + y = −1 40   x + y + x − y = 42 (  x + x  log x  2 x − = y − 3x 41  y y 2 − = 3x − ) −3x − x + + x > 3x.2 x -3x − x + + ( x ) 3x 43 ( 2cos3 x + 6cos x + 1) = 162cos x − 27 45 47 x x + x =  + 8log 2 ng 39 log 22 x + x.log oc ) bo cu ( c x  33 ( log x ) + x log ( x + 3) = log x  + 2log ( x + 3)  2    y + y2 +  2 ( x − y ) x + y + xy − = 6ln    x + x2 +  34      x − x + = y 1 + x  x − 16 y − cos x − cos y =  1 + y = e y 36  35  x  x − xy + y =    y = − 2x − x + log ( x + 3) > 36 37 cos5 x + cos x = sin x − cos x x +1 x 44 x − + x − 3x + = x + + x + = 3x + 2 x + x + − 16 x + =1+ x 48 ( x + 1) log32 x + x log3 x − 16 = ( x − y ) x − y =  49  2 ( x + y ) x + y = 15  x + x ( 3x + y ) = 18 50   x + x + y − = 51 e x = + ln ( x + 1) 52 ( ( ) ) ( ( ) ) + x + = x3 + 2 Sưu tầm: Hồ Văn Diên – THPT Thái Lão Truy cập www.khongbocuoc.com để download thêm tài liệu học tập khác www.VNMATH.com  xy − 18 = 12 − x 2  6 x − 3xy + x + y = 53  54  y2  x + y =  xy = +  x + y −1 4 + 3.42 y −1 = x x 55 + ( x − 12 ) + 11 − x = 56   x + y = − log x  π π + cos x =  − ;   2 57 61 60 15 x5 + 11x3 + 28 = − 3x  x ( y − ) = ( x + )( y − ) 62  ( y + )( x − 3) = ( y + 3)( x − ) oc ( )  = + − x2  bo cu (1 + x ) − 10 − x = x − 63 x = 4 x + + 64 2cos x + sin x cos x + = sin x + cos x ( ) 67 x x − = 69 16 x3 − 24 x + 12 x − = x 71 cos6 x − cos x = (1 + cos3 x ) 68 x3 − 3x = x + 70 2log t = log ( + t ) 1 x −1 − 1− > x x x  x3 + x ( y − z )2 =   59  y + y ( z − x ) = 30   z + z ( x − y ) = 16 2  x y − x + y = 58  2 x + x + y − 12 x + 13 = 65 + − x  (1 − x ) −  x +1 =x− 66 x +1 − − x x− om c 57 e tan on g    81  72  sin x +  +  cos x +  = cos x sin x   cos3 x   73 sin x − cos x = + ( sin x − cos x ) 74 x3 + (1 − x ) = x (1 − x ) 75 kh x − x + 10 + x = 3 x − x + x − x +  1 x + y  xy  2 x + y + = 16  x  +  =  x + y x + y     77 76    x + 2x = x + x − y 4  x + y  8 y  y  − x + y  = 3y     x   xy − x + y = 2 + y = y − x − y 78  79  x + 12 x + x = − y + y +   x + x − y = x + 3y −  2 81 x + + x − = x − 80 x + x + = + x + x − x − x Sưu tầm: Hồ Văn Diên – THPT Thái Lão