Chủ đề: PT VÀ BPT VÔ TỶ

Chuyờn I S S CP Luyn thi i hc 2011 PHNG TRèNH- BT PHNG TRèNH Vễ T Ch : I- H thng cỏc dng toỏn c bn: Dng 1: Dng 2: ỡ g( x ) ùỡ f ( x ) ( chọn g( x ) ) f ( x ) = g( x ) f ( x ) = g( x ) ợ f (x) = g (x) ợù f ( x ) = g( x ) Dng 3: Dng 4: ỡ g( x ) ỡ g( x ) f ( x ) > g( x ) f ( x ) g( x ) ợ f ( x ) > g( x ) ợ f ( x ) g( x ) Dng 5: Dng 6: ộ ỡ g( x ) Ê ộ ỡ g( x ) Ê ờớ ờớ ợ f (x) > ợ f (x) f ( x ) > g( x ) ờờ f ( x ) g( x ) ờờ ỡ g( x ) ỡ g( x ) ờớ ờớ ờở ợ f ( x ) > g2 ( x ) ởờ ợ f ( x ) g ( x ) Dng 7: Dng 8: ỡ g( x ) > ỡ g( x ) > ù ù f ( x ) < g( x ) f ( x ) f ( x ) Ê g( x ) f ( x ) ù ù f ( x ) Ê g2 ( x ) ợ f (x) < g (x) ợ II- LUYN TP: Phng phỏp 1: BIN I TNG NG Bi 1: Gii cỏc phng trỡnh sau: 1) x + + x + - x + = 2) x + = - x + 3x + 3) x - - 3x - - x - = 4) 3x - - - x = x - 5) (x - 3) x - = x - 6) 3x - x + = x - 6) - 1- x = - x 7) 3x - 3x - = 8) x - x -1 + x + - x -1 = 9) x + x -1 - x - x -1 = Bi 2: Gii cỏc bt phng trỡnh sau: 1) - x + x + + 2(2 x - 1) > x + - - x > 2x - 3) 5) - 2- x < 2- x 7) 9) 2) 3x + 13x + + - x 4) 6) 2x + x2 + > x + x - 16 + x-3 > x-3 1 - < x2 x x-3 - 4x 2x + 8) x + + x + = x + 11 10) ( x - 3) x - Ê x - Giỏo viờn: Lấ B BO T Toỏn THPT Phong in Chuyờn I S S CP Bi 3:** Gii cỏc bt phng trỡnh sau: 1) ( x - ) x - x + Ê 3) ( x - 1) ( x - 2) x( x + 2) 5) ( x - 2) x + Ê x - 2 2x > 2x + 2x + -1 2x2 10) Ê x + 21 (3 - + x ) 7) Luyn thi i hc 2011 2) ( x - x + 3) x - > 4) ( x - x) x - x - 4x2 6) < 2x + (1 - + x ) 8) 4( x + 1) < (2 x + 10)(1 - + x ) 11) 2x2 Ê x + 21 (3 - + x ) 12) 4( x + 1) < (2 x + 10)(1 - + x ) 13) x + x ( x + 4) x - x + Phng phỏp 2: T N PH t n ph loi I: Bi 1: Gii cỏc phng trỡnh sau: 1) x + 3x + + x + x + = x + x + 3) x + 10 x + = - x - x 2) 3x + x + - 3x + x + = 4) ( x + 1)( x + 4) = x + x + 28 ) 5) ( x - 3) + x - 22 = x - x + 6) x ( x + 5) = 23 x + x - - 7) x - x + = x - x + 8) - (4 - x )(2 + x ) = x - x - 12 t n ph loi II: Bi 2: Gii cỏc phng trỡnh sau: 1) + x - x = x + 1- x 3 x + + x - = x + x - 16 - 5) 2) 4) x + x = 2x + +4 2x x + + x - + 49 x + x - 42 = 181 - 14 x 6) x + + x + - x + = 8) x + + x + = x + 2 x + x + -2 7) x - + x - = x - + x - x + 9) x - + x - 3x + = x x +1 -2 =3 x +1 x Bi 3: Gii cỏc bt phng trỡnh sau: 7) x( x + 3) Ê - x - 3x 9) x - x - x - x + 12 x x +1 -2 >3 x +1 x 8) ( x + 4)( x + 1) - x + x + < 10) x( x - 1) + > x2 - x + 15) x > 1+ x -1 < 2x + +2 2x x 16) ( x + 1) + ( x + 1) + x x + > 17) x - + x + + ( x - 1)( x + 3) > - x 18) x + - x Ê x - x 11) Giỏo viờn: Lấ B BO 13) x + T Toỏn THPT Phong in Chuyờn I S S CP Luyn thi i hc 2011 x 35 20) x + > x - 12 x + + - x - < + ( x + 5)(- x - 3) 19) 23) x - Ê x x + x 24) x - x x - x 25) (4 x - 1) x + Ê x + x + 26) x + 12 x + - x - > x + x + + - x - < + ( x + 5)(- x - 3) MT S BI TP Cể PHNG PHP GII C SC Bi 1: (ng dng bit s D ) Gii cỏc phng trỡnh sau: 2x2 - 6x + - x Ê x - 27) 28) 1) (4 x - 1) x + = x + x + 2) 2(1 - x ) x + x - = x - x - 3) x + x + 12 x + = 36 4) + x - = 3x + - x + - x 6) + x - = x + - x + - x 5) x - x = 2 x - Bi 2: (Lng liờn hp) Gii cỏc phng trỡnh sau: 1) 3) (1 - 4x + 2x ) = 2x + x + - 3x - = x +3 2) 3x - x + - x - = ( x - x - 1) - x - 3x + 4) x - + x - 3x - = x + x + + x - x + Bi 3: (Kh tr tuyt i) Gii cỏc phng trỡnh sau: 1) x + - x -1 + x + - x -1 = x + x -1 + x - x -1 = 2) 3) x + + x - + x - - x - = 2 x +3 4) x + x - - x - x - = 6) x + = x + + 5) x - 2x + = - x 7) x - 4x - + x + 4x - = 8) x + 15 - x - + x + - x - = Bi 4: (K thut a v phng trỡnh ng cp) Gii cỏc phng trỡnh sau: a) ( x + ) = x + b) x + x - = x - MT S THI I HC- CAO NG 1: (Khi D- 2002) Gii bt phng trỡnh: ( x - x ) x - x - 2: (D b- 2002) Gii bt phng trỡnh: 3: (D b- 2002) Gii phng trỡnh: x + 12 x - + x + x + + x - = x - 12 + x - 16 ( x - 16 ) 7- x x -3 x -3 5: (D b- 2004) Chng minh vi mi m , phng trỡnh sau luụn cú nghim: 5ử ổ x + ỗ m - ữ x + + - m3 = 3ứ ố 6: (Khi D- 2005) Tỡm m phng trỡnh sau cú nghim: 4: (Khi A- 2004) Gii bt phng trỡnh: m ( + x -3 > ) + x2 - - x2 + = - x4 + + x2 - - x2 Giỏo viờn: Lấ B BO T Toỏn THPT Phong in Chuyờn I S S CP 7: (Khi A- 2005) Gii bt phng trỡnh: Luyn thi i hc 2011 5x - - x - > x - 8: (Khi D- 2005) Gii phng trỡnh: x + + x + - x + = 9: (Cao ng- 2009) Gii bt phng trỡnh: x + + x - > x + 10: (Khi D- 2005) Gii phng trỡnh: x - + x - x + = 11: (D b- 2005) Gii phng trỡnh: x - - - x = x - 12: (D b- 2005) Gii bt phng trỡnh: x + - - x x - 13: (D b- 2005) Gii bt phng trỡnh: x - x + - x + Ê 14: (Khi D- 2006) Tỡm m phng trỡnh sau cú hai nghim thc phõn bit: x + mx + = x + 15: (D b- 2006) Gii phng trỡnh: 3x - + x - = x - + 3x - 5x + 16: (D b- 2006) Gii phng trỡnh: x + - x = x - + - x + x - + 17: (Khi A- 2007) Tỡm m phng trỡnh sau cú nghim: x - + m x + = x2 - 18: (Khi B- 2007) Chng minh rng vi mi giỏ tr dng ca tham s m , phng trỡnh sau luụn cú nghim thc: x + x - = m ( x - ) 19: (D b- 2007) Tỡm m phng trỡnh: m ( ) x - x + + + x(2 - x) Ê cú nghim x ẻ ởộ0;1 + ựỷ 20: (D b- 2007) Tỡm m phng trỡnh: 21: (D b- 2007) Tỡm m phng trỡnh: ỳng nghim x + - x = m cú nghim x - - x - + x - x - + = m cú 22: (D b- 2007) Tỡm m phng trỡnh : x - 13x + m + x - = cú ỳng nghim 23: (Khi A- 2008) Tỡm m phng trỡnh sau cú hai nghim thc phõn bit: 2x + 2x + - x + - x = m 24: (D b- 2008) Gii phng trỡnh 2x + + - 2x = 25: (D b- 2008) Gii bt phng trỡnh : ( x - 1) 2 3x +1> 1- x 1- x 26: (D b- 2008) Gii phng trỡnh : 10 x + + 3x - = x + + x - 27: (D b- 2008) Gii bt phng trỡnh : ( x + 1)( x - 3) - x + x + < - ( x - 1) 28: (Khi A- 2009) Gii phng trỡnh: 3 x - + x - - = x- x 29: (Khi A- 2010) Gii bt phng trỡnh: - ( x - x + 1) 30: (Khi B- 2010) Gii phng trỡnh: Giỏo viờn: Lấ B BO x + - - x + x - 14 x - = T Toỏn THPT Phong in ... x - + x + + ( x - 1)( x + 3) > - x 18) x + - x Ê x - x 11) Giỏo viờn: Lấ B BO 13) x + T Toỏn THPT Phong in Chuyờn I S S CP Luyn thi i hc 2011 x 35 20) x + > x - 12 x + + - x - < + ( x + 5)(-... Gii bt phng trỡnh: m ( + x -3 > ) + x2 - - x2 + = - x4 + + x2 - - x2 Giỏo viờn: Lấ B BO T Toỏn THPT Phong in Chuyờn I S S CP 7: (Khi A- 2005) Gii bt phng trỡnh: Luyn thi i hc 2011 5x - - x -... x + 1) 30: (Khi B- 2010) Gii phng trỡnh: Giỏo viờn: Lấ B BO x + - - x + x - 14 x - = T Toỏn THPT Phong in