CHUYÊN ĐỀ PHƯƠNG TRÌNH VÀ BẤT PHƯƠNG TRÌNH BÀI TẬP SỬ DỤNG ẨN PHỤ (PHẦN 1) ------------------------------------------------------------------------------------------------------------------------------------------Bài 1. Giải phương trình bất phương trình sau tập hợp số thực 1, x − + x = 2, − x + x − x + x − x = 3, x + x + < x ( + x ) + 4, x ( x − ) x − x + ( − x ) < 2 5, ( x + 1) + ( x + 1) + 3x x + > 6, x + x − + x3 + x + = 7, x + x + − 2 x + x − = 8, x + 21x + 18 + x + x + = 9, x + x + < − x − x 10, x − 12 x − x − 12 x + 11 + 15 = 11, x ( x + 3) > − x − x 12, + ( x + 1)( + x ) ≤ x + 3x 13, x − 34 x + 48 ≥ ( x − )( x − 32 ) 14, x + 3x + 12 = x ( x + 3) − 15, x − x + 15 = − x − x + 16, x + x + − x + x + > 17, x + x = x + x + − x 18, x + x = ( x + x + ) + 19, x2 + x + = x ( x + 2) − 20, 18 x − 18 x + = 3 x − x + 21, 3 x − 3x + = x − x + ( 22, x − x + = − 3x − x + ) 23, x ( x − 1) − x > x − x + 24, x + 15 x + x + x + = 25, ( x + )( − x ) = x + x 26, x + 10 x + > − x − x 27, x + x − x − = 10 x + 15 28, ( x + 1)( x + ) ≤ x + x + 28 CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 2. Giải phương trình bất phương trình sau tập hợp số thực 1, x − x = −2 + x + − x 2, ( − x ) + x − 22 = x − 3x + 3, x ( x + ) > x + x + − ( − x )( x + ) ≤ x − x 5, x + x + = ( x + ) x 4, 12 − 6, x2 − x + + x2 − x + = 7, x + x + + x + x + = x + x + 19 8, x + x + − ( x + x + 1) = x + ( x + 1) 9, (1 + x )( − x ) > + x − x x+6 11 28 11, x − 3x − x + x − = − x 12, x x + + x + x = 10, x + − x − x + = 13, x x + + ( x + ) = 20 14, x + x = x + x − 15, + x +2 =3 x x +1 16, x +1 x −1 + =2 x −1 x +1 17, x +8 3+ x + =5 x x 18, 4x + 1 + =5 4x x 19, x2 − x + = x − x2 20, + x − + − x − = 21, − x − x + − x − x = 22, + x + − x > 3− x − 23, 3 x + x − x − x = 24, x + x + = ( x + x ) + 25, x + x + < x + 14 x − 26, x2 + x + ≤ x x2 + x + +1 x CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 3. Giải phương trình bất phương trình sau tập hợp số thực 1, x + + x + = x + x + 10 x + − 16 2, x + + − x + + 16 x − x > 13 12 − x x − 82 + ( x − 2) < 12 − x x−2 3x 4, > −1 1− x − x2 5x 5, ≤ +2 2− x − x2 3, (12 − x ) 6, x + 16 + x = 7, ( x + 16 + x 2 ) + 32 1− x + x + =2 2+ x 1− x 8, + x − − x + 4 − x = 10 − x x 9, x + 10, =2 2x 1 + =2 + 2x x +1 x + + x − = x + x − 16 11, 12, x −1 x −1 + x = x + 13, x + x x −1 > 35 12 x + − 12 − x = − x + 11x − 23 14, 15, + x − − x = − x + x + 63 16, − x + x − − 4 x − x − + ≥ 17, x − x2 −1 + x + x2 −1 = 18, ( x + 1) − x = x + − x 19, 20 + x 20 − x − = x x 20, x2 − − x + = x−2 + x+2 21, x + 17 − x + x 17 − x = 22, x + − x = + 3x − x 1 −2 +1 > x +1 x +4 24, x + = x − x x 23, − CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 4. Giải phương trình bất phương trình sau tập hợp số thực 1, x + x x − = x + x 3, x + x − x = + x 4, − x + − x = 5, + 6, x − x2 = x + − x x + + x + x + x = 35 − x 7, x + + + x = x + 2 x + x + − 8, x + 9, x > 2x + +4 2x x −1 + x + + ( x − 1)( x + 3) + x = 10, x − + x − = x − + x − x + 11, + x + − x = + (1 + x )( − x ) 12, + x + − x = + ( + x )( − x ) 13, x + + − x + 2 + x − x = − x 14, x + − x + x − x = 15, x + − x = + x − x2 16, x + + 6− x = 8− 17, (2 − x) ( x + )( − x ) + ( + x ) = + ( + x )( − x ) 18, + x + − x − (1 + x ) 19, − x + x + = x − x + 18 = 20, 21, − x + 8− x =3 1+ x (1 − x )(1 + x ) + x − x + 15 x − x + 11 x −1 =3 x−2 ( x − 1)( x − ) + ( x − ) x+2 = −3 x−2 8x2 23, + x − − x = + − x2 22, x − + ( x − ) x − 4− x = 24, 25, ( 2(2 − x) + 4x − x2 )( ) x + − x −1 + x2 + x − = 26, x + x ≤ x + − CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 5. Giải phương trình bất phương trình sau tập hợp số thực x +1 = −3 1, ( x − 3)( x + 1) + ( x − 3) x−3 2, − x − + x + − x = − x 3, x − = ( x + ) x+3 x −3 4, x − = x + x + x −1 x +1 = + + 2x − x2 x +1 + − x 5, 6, x − x = ( − x ) x + 7, x − x + = ( − x ) + x 8, x − x + 15 = ( − x ) + x 9, x − = x x + x 10, x + x = ( x + ) x − x + x + = x2 + x + 11, 12, x = 3x − 14 x + 14 13, x + + x − + 49 x + x − 42 < 181 − 14 x 14, ( + x ) ( − x )(12 + x ) + x = 28 x − 3x + = x2 + 2x −1 15, − 2x ) ( 16, x + 14 − x + x x + x − 14 x ( x + ) + 24 = 17, x − x − + 16 x = ( )( ) 18, x + 15 x + 36 x + x + = 520 x 19, x − 16 = ( + x ) x+4 x−4 1  20,  x −  x + 3x + = x 3 9  21, x − x + x = ( x − x ) 22, x − 11x + + ( x − ) x − x + = 23, 5x2 − x + = x2 + x + − 4x 24, x − 11x + = ( − x ) x + x + 25,5 16 − x − 16 − x =4 CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 6. Giải phương trình bất phương trình sau tập hợp số thực x2 + x x2 − x x −1 ≤3 x +1 15, x + ( x + 1) 16, x − x − x x2 − ≥6 x 17, x − 3 x − x − ≤ x + 18, ( x + x + ) = + x 19, ( ) x −1 + + x −1 = − x 20, x − x + ( − x ) x +1 = 12 x −5 21, x − x + ≥ x − x − x + 22, − x2 x x − x + 16 + +1 ≤ 2 x x (4 − x ) − x2 CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 7. Giải phương trình bất phương trình sau tập hợp số thực x +1 1, x + < ( x + ) x+2 2, ( x − 3x + ) < x − x − 3, ( x + x + ) ≤ ( x + 3) + x 4, x− x − ( x − x + 1) ≥1 x −2 5, ( x2 − x + 4) − x 3x − x 6, ≥ ( x + 13 x + 16 ) − 12 ≤1 7, x + 12 x + − x ≤ − x 8, 9, x +1 x + 5x + + x ( )( x +1 x +3 x − 10 x + ≤1 ) >3 ( x − 1)( x − ) ≤ x − x − 11, x − x + ≥ (1 + x ) x 12, + x = x ( x − ) 10, 13, x ≤ x+2 ( x + 1)( x + ) x ≥ x + 10 x + x + 2 x2 − 5x + 15, . ≥ x 3x − 4x2 − 2x + 16, ≤ x 2x +1 14, 17, ( x − x + ) + x ≤ ( + x ) 18, x + 15 x + ≤ x ( + x ) 19, x3 − x − ≥ 2x x −7 20, ( x − ) ≤ ( x + ) x 21, + ( x − 2) ( + x2 ) ≤ x + x 22, x + x + ( x − 10 x + 1) x ≤ + x CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 8. Giải phương trình bất phương trình sau tập hợp số thực 1, x − x + 13 ≤ ( − x ) x + 2, 15 x − x + 13 + (12 x − ) x + = 18 x − x + 19 > + x2 − 12 x 18 x + 15 x − 4, = 3x + − − 12 x 3, 5, x − x + + ( x − ) + x = 6, ( x + 1) + ( − x ) x + = x − 7, ( x + 1) x2 − 5x + −1 = 2x − 2x + +1 8, + x ( x − ) + ( x − ) x − = 9, (1 + x ) = ( x + 1) x + 10, x + + x − x + = x 11, x − x = + x − x + 12, x ( x − 1) ≤ x ( x + 1) 13, x + x2 + x − = x + 14, 3x − 28 + x + x − = 15, 23 x − 32 x = x 3x + x + + 16, x + x − = 2 x + x + x − − 28 x 24 x − 2 − x − x2 x 18, = ( x − 1) + + 5x2 13 19, 3x + x + + x x + x + = 17, x + < 20, x2 − 5x + + x2 + x − x2 + 2x − ≤ − 2x x + x + 10 ( − x ) ≥ −1 x − x + 26 − 2x x + 17 22, > x+5 − x 16 x + − x (1 + x )( x − ) 23, ≤ 11 − x x − 3x + x +3 24, = x + −1 4− x 21, ( ) CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 9. Giải phương trình bất phương trình sau tập hợp số thực 1, ( − x ) + x − x ≤ 16 2, x − x + x − x > 3, x + x + + x + ≤ x x2 + 6x + + x ≥1 4, x −1 5, x2 + x + − x + ≤ −1 x−2 6, x2 − 5x + − x + ≤1 1− x x + x − 16 7, ≥6 ( x + 1)( x + ) + x − 2 ( x + 1) + ≤ + x 8, x2 + 3x + + x 15 + ( x − 1) 9, x + 3x + − x ( )( 10, x + ) ≥4 x +2 ≤ ( )( x +1 (1 + x ) x +2 ) x2 + 3x + − x 11, x − 3x + − x − ≤1 2x − 12, x − x + − x + 15 =2 7−x 13, x + 24 x + 26 ≤ x (1 − x ) 14, x + 24 x + 26 = ( − x ) x   15, ( − x ) ≥ +  x − +  x − x   4  16, ( x − ) < 16 + 3x −  x − + 33 x  36   17, 11x + 19 x −  x − = 27 x x   − x x2 1  19,  −  x − ≤ ( x − 3) + x  1  20, 14 x < + 10  − x  − x x  18, x − x + = 10 ( x − 1) 21, x − x − 10 x − x − < + x − x2 x CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 10. Giải phương trình bất phương trình sau tập hợp số thực 1, x + 12 x ≤ 18 x + ( x − ) x − 2, x ( x − 3) + 21x + ( − x ) x − = 3, x − ≥ (1 − x ) − x x 4, x ( − 25 x ) + ( − x ) − x = − x 2x −1 1− 2x ≤ x −1 x ( x − 1)( − x ) 6, ≥ 2 − 3x 3x −   7, x +  x − + 36  x − + x ≤ 18 x   5, 8, x + ( x − 16 x + 12 ) x − + x = x 9, ( x + 1) + 10, 11, x −1 .( x − 2) ≥ x x + x + x + ( x + 1) ≥ x x + ( x + 1) x ( 3x2 + x − 4) 3x + x − 12, ( 3x + 12 x + ) = ( x − 1)( x + ) (1 + x )( + x ) ≤ x ( 3x + x + ) 13, x + x + = x + 14, x + x + x + = ( x + 1) x + 15, x + 19 x + 11 ≤   +  x + + 18  x − x  x  16, x + 13 x − 53x + 39 ≤ ( x − x − 15 ) x − 1  17,  x − +  − x ≥ x − 10 x + x  18, ( x − 3) + ( x − ) x − = 19, x + + x − = x − x − + + x 20, x + 10 x − = + x − + + x 21, 12 x − + 13x < + 12 x − + x + 22, 10 x − + x − = + x + 10 x − 23, x + 24, 12 6  = +  −  x2 + x + x x  x + x3 − x − x + = x2 + x + 2x + 2x − CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM 10 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 11. Giải phương trình bất phương trình sau tập hợp số thực 1, x + + ( x − )( − x ) = 3x − + − x 2, 11 − x + 10 − x = x + + − x 3, ( x − )( x − ) = − 2x ( − 2x − 2x −1 ) 4, ( x + x + 12 ) − − x = x + 10 x 5, − − x ≤ ( x + 3)( x + 3) x2 + 8x + − 2x x − x + 28 6, = 3x + 3x − x − x + 55 7, ≥ ( − x )( − x ) − + 3x 8, x + 17 + 14 x + = x + x + + − x 9, x3 + 3x − x + = 1+ x − x − 3x 10, x + x − x + ≤ ( x + x − ) + x 11, ( x + x − ) + x + x + x − x + 12 > 10 ( x − 1) x − + x x3 + 3x − 3x 13, 10 3x − ≥ 3x − ( x − 2) x + 25 x − 68 x + 12 = 14, x + 20 x − 5x −1 + x + 44 x − 33 x ≤ ( x + x − 3) x − 15, 12, x + x ≤ x + 22 x − 11x >6 x− 2 2x + 2x −1 x + x − 28 x + 12 x − +1 17, ( x − 3) ≤ x2 + x − x + 10 x − 23 x + =6 x−2 18, + x2 + x − 16, ( ) 19, (13 − x ) x − + ( x − 3) − x = + 16 x − x − 15 ( 20, (13 + x ) x − + ( x + ) x + ≤ x + + x − ) 21, ( x − 1) x + + ( x + 1) x − = 22, ( x − 1) x − + ( x + 1) x + = 23, (13x + 1) + x = ( x + 3) x + 24, x = 19 + x + x x + CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM 11 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 12. Giải phương trình bất phương trình sau tập hợp số thực 1, x + = ( x + − 12 x ) x + + 12 x + 18 x 2, ( 3x + x + ) x + + x + 12 x + 18 x = 3, x + 12 x + ( x + x − 24 ) x − = + 36 x 4, ( x + x + ) x + = 27 ( x + 1) + x 5, 2 + x ≥ 6, x + < x + 12 x + 24 x + 27 3x + x + 8 x + x ( x + ) + 27 12 x + x + 7, x + x + x = ( x + ) x + 8, x + x + 12 x + ( x + ) x = 20 9, x + x + (12 x + x ) x = + x 10, 3x x − x + + x2 = x x  26  11, x + 15 ( x + 1) + x  3x + 10 +  ≤ x x  3x +1 < 12, 3− x − x2 − 4x − 2x + ≥2 − x2 − x2 5x + 3x + ≥5 14, ( x + 1) ( x3 − 1) 13, 15, x2 − +1 ≥ − x (6 − x) x > − x3 5x +9 x3 − 2 − x3 12 x + 14 ≤ 17, 3 1− x − x3 1  18, x + 12 x + 16  − 1 − x ≤ 12 x  16, 19, 16 x < (11x − x + ) 20, 11 + x ( x + 1) ≤ ( x − 1)( + x ) 16 24 x2 + x +1 11 21, (12 x − 25 x + 12 ) + x + 16 (1 − x ) = 22, x3 − x ≤ x2 −1 3x − CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM 12 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 13. Giải phương trình bất phương trình sau tập hợp số thực 1, x + x + > x ( x − 3) 2, x − x + 23 > x −7 x−2 ( ) 3, x + x + ≤ x − ( x − ) ( ) 4, ( + x )( + x ) ≤ x − ( x − ) x2 + 8x ≥ x +1 x −1  1 6, x + 14 + = 10 1 −  x x  x 5, 7, ( + x ) + 10 ( − x ) x ≥ ( ) 8, x + 11x < 3 x + ( x − 3) 9, x + 3x + + x − ≤1 x −3 10, 2x2 + x + + >1 x−x 11, x + 10 x + ≤1 x−3 x + 12, x + ≤ x + ( x + x − ) 13, x + 3x + + x + 3x ≥ 14, x + 12 x + ≥ x x + 15, x + 15 x − x x x2 −1 ≥1 x 16, − x − x2 ≤ x + 10 x x 17, > x − x2 + 14 x + x x 18, ( x − 3x − 1) 3x − 19, x − + 2x ≤ x 2x ≥ x 3x + − x2 20, x + ≥ x − x − 29 x + 36 21, ( x + − x ) x + + 12 x ≤ x + x x2 + 9x + x+ ≥2 22, x x + x + 12 CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM 13 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN BỘ BINH Bài 14. Giải phương trình bất phương trình sau tập hợp số thực x +1 1, x − = ( x + 1) x −1 1 +3 ≤ x− +2 x x 3, + 3x − x ≥ + x + x 4, + x − x ≤ + + x x 5, + x + > 5 + x − x x 2, x2 + 6, x + = ( x − ) x 7, x + x ≤ ( x − ) x +1 x 8, x + 10 x = x x − 9, x + 12 x = x 10, x + ( x2 − +1 x ) x +1 +1 = 11, x + x − − x 12, 3x x2 − =0 x 3x − x3 + = x3 + 3x + x3 13, x − x + x + ≤ x − x + 14, x (1 − x ) + x + ≤ x ( x + x + 3) 1− x x + 24 x + 25 15, ≤4 x x −5 x − x + 16 16, ≤5 x x−4 17, x + 3x − x + + ≤ x 18, x − x + + x ≤ − x 19, x + x + + x + ≤ 11 x 20, x + 12 x2 + − x ≤ x −1 21, x2 + x + ≥ x −2 x −1 22, x − 20 x + 18 − x + x [...]... + 1 ≥5 14 , ( x + 1) ( x3 − 1) 13 , 15 , x2 − 8 6 +1 ≥ 4 − x (6 − x) x 4 > 2 − x3 5x +9 x3 − 2 2 − x3 12 x + 14 ≤ 17 , 3 3 1 x 1 − x3 1  18 , x 2 + 12 x + 16  − 1 1 − x ≤ 12 x  16 , 3 19 , 16 x 3 < (11 x 2 − x + 2 ) 20, 11 1 + x 2 ( x + 1) 3 ≤ ( x − 1) ( 2 + x ) 16 24 x2 + x +1 11 21, (12 x 2 − 25 x + 12 ) 1 + x + 16 (1 − x ) = 0 3 22, 6 x3 − 5 x ≤ 2 x2 1 3x 2 − 1 CREATED BY HOÀNG MINH THI; XYZ14 319 88@GMAIL.COM... ≤ 1 2 x 3 + 22 x − 11 x >6 x− 2 2 2x + 2x 1 3 2 x + 5 x − 28 x + 12 x − 2 +1 17, 6 ( x − 3) ≤ x2 + x − 2 x 3 + 10 x 2 − 23 x + 2 =6 x−2 18 , 1 + x2 + x − 2 16 , ( ) 19 , (13 − 4 x ) 2 x − 3 + ( 4 x − 3) 5 − 2 x = 2 + 8 16 x − 4 x 2 − 15 ( 20, (13 + 4 x ) x − 1 + ( 4 x + 9 ) x + 1 ≤ 6 2 x + 1 + 2 x 2 − 1 ) 21, ( 2 x − 1) x + 1 + ( 2 x + 1) x − 1 = 1 22, ( 4 x − 1) 2 x − 1 + ( 4 x + 1) 2 x + 1 = 4 23, (13 x... (13 x + 1) 1 + x = 2 ( 7 x + 3) x + 1 24, 8 x = 19 + x 3 + 6 x x + 1 CREATED BY HOÀNG MINH THI; XYZ14 319 88@GMAIL.COM 11 TRUNG ĐOÀN 1 – SƯ ĐOÀN 8 – QUÂN ĐOÀN BỘ BINH Bài 12 Giải các phương trình và bất phương trình sau trên tập hợp số thực 1, 8 x 3 + 8 = ( 2 x + 3 − 12 x 2 ) 2 x + 3 + 12 x 2 + 18 x 2, ( 3x 2 + 9 x + 5 ) 3 x + 2 + x 3 + 12 x 2 + 18 x = 1 3, x 3 + 12 x 2 + ( 6 x 2 + 8 x − 24 ) x − 3 = 1 +... 2 1 2 x −3 10 , 2x2 + 7 x + 8 + 2 >1 2 x−x 11 , 2 x 2 + 10 x + 8 1 x−3 x + 2 12 , x + 3 ≤ 3 x + 2 ( x 2 + 7 x − 9 ) 13 , x 2 + 3x + 2 + x 2 + 3x ≥ 4 14 , x 2 + 12 x + 2 ≥ 7 x x + 15 , x 2 + 15 x − 8 x 2 x x2 1 1 x 16 , 1 − 3 x 1 − 2 x2 ≤ 2 x 2 + 10 x x 17 , 3 > 5 x 3 − 4 x2 + 14 x + 4 x 2 x 18 , ( 3 x 2 − 3x − 1) 3x − 19 , 4 x − 1 + 2x ≤ 0 x 1 2x ≥ x 3x + 1 − 4 x2 20, x + 3 ≥ 6 x − 4 x 2 − 29 x + 36 21, ... x − 2 ) x 1 +1 x 8, x 2 + 10 x = 7 x x − 9, x 2 + 12 x = 8 x 10 , x + 1 ( x2 − 1 +1 x ) x +1 +1 = 2 11 , x 2 + 8 x − 2 − 9 x 12 , 3x 3 x2 − 2 =0 x 3x 2 − 4 x3 + 5 = 5 x3 + 3x 2 + 5 x3 13 , 3 x 2 − 2 x + x + 3 ≤ 5 x − x + 1 14, x 2 (1 − x ) + x + 9 ≤ x ( x 2 + x + 3) 1 x x 2 + 24 x + 25 15 , ≤4 x x −5 x 2 − x + 16 16 , ≤5 x x−4 17 , 7 x + 3x 2 − x + 3 + 1 ≤ x 18 , 3 4 x 2 − 2 x + 4 + 6 x ≤ 1 − x 19 , 2 x 2.. .Bài 11 Giải các phương trình và bất phương trình sau trên tập hợp số thực 1, x + 7 + 2 ( 3 x − 2 )( 3 − 2 x ) = 5 3x − 2 + 5 3 − 2 x 2, 11 − 3 x + 10 1 − x = 5 x + 1 + 4 1 − x 2 3, ( x − 2 )( x − 7 ) = 5 − 2x ( 2 − 2x 3 − 2x 1 ) 4, ( x 2 + 5 x + 12 ) 1 − 1 − 2 x = 4 x 2 + 10 x 5, 2 − 1 − 2 x ≤ 2 ( x + 3)( 2 x + 3) x2 + 8x + 2 9 − 2x x 2 − x + 28 6, = 3x 1 + 3x − 1 2 3 x − 7 x + 55... 12 TRUNG ĐOÀN 1 – SƯ ĐOÀN 8 – QUÂN ĐOÀN BỘ BINH Bài 13 Giải các phương trình và bất phương trình sau trên tập hợp số thực 1, x 2 + 4 x + 9 > 7 x ( x − 3) 2, x 2 − x + 23 > 7 x −7 x−2 ( ) 3, x 2 + 7 x + 6 ≤ 8 x − 1 ( x − 2 ) ( ) 4, ( 3 + x )( 4 + x ) ≤ 4 2 x − 1 ( x − 2 ) x2 + 8x ≥ 9 x +1 x 1 1  1 6, x + 14 + = 10 1 −  x x  x 5, 7, ( 4 + x ) + 10 ( 4 − x ) x ≥ 0 2 ( ) 8, x 2 + 11 x < 3 3 x + 1. .. 6 x − 4 x 2 − 29 x + 36 21, ( x 2 + 2 − 8 x ) x + 2 + 12 x ≤ x 2 + 2 x 4 x2 + 9x + 4 x+ ≥2 22, 2 x 3 x + 2 x + 12 CREATED BY HOÀNG MINH THI; XYZ14 319 88@GMAIL.COM 13 TRUNG ĐOÀN 1 – SƯ ĐOÀN 8 – QUÂN ĐOÀN BỘ BINH Bài 14 Giải các phương trình và bất phương trình sau trên tập hợp số thực x +1 1, 2 x 2 − 1 = ( x 2 + 1) x 1 1 1 +3 ≤ x− +2 2 x x 1 3, 2 1 + 3x − x 2 ≥ + x + 3 x 2 4, 3 2 + 4 x − x 2 ≤ + 4 +... − 1 + 3x 8, 5 x + 17 + 14 x + 1 = 6 x 2 + 4 x + 3 + 7 3 − x 9, x3 + 3x 2 − 4 x + 6 = 1+ x 6 − x − 3x 2 10 , x 3 + 3 x 2 − x + 6 ≤ ( 3 x 2 + x − 5 ) 2 + x 11 , ( 3 x 2 + 2 x − 7 ) 1 + 2 x + x 3 + 6 x 2 − 5 x + 12 > 0 10 ( x − 1) x − 1 + 1 x x3 + 3x 2 − 3x 13 , 10 3x − 1 ≥ 3x − 1 3 2 5 ( x − 2) x + 25 x − 68 x + 12 = 14 , 2 5 x + 20 x − 4 5x 1 + 3 x 3 + 44 x 2 − 33 x ≤ ( x 2 + 4 x − 3) 4 x − 3 15 , 6 12 ,... x + 6 ) x + 2 = 27 ( x + 1) + x 3 2 5, 2 2 + x ≥ 6, 5 x + 5 < x 3 + 12 x 2 + 24 x + 27 3x 2 + 4 x + 8 8 x 3 + 6 x ( x + 5 ) + 27 12 x 2 + x + 5 7, x 3 + 3 x 2 + 3 x = ( 3 x + 4 ) x + 7 8, x 3 + 6 x 2 + 12 x + ( 4 x + 2 ) x = 20 9, 7 x 3 + 3 x 2 + (12 x 2 + x ) x = 1 + 3 x 10 , 3x x − 5 x + 3 9 + x2 = x x 3  26  11 , x 2 + 15 ( x + 1) + 2 x  3x + 10 +  ≤ x x  3 3x +1 < 12 , 2 3− x 3 − x2 9 − 4x 3 . 2 2 3 2 2 2 2 1 6 1 2 5 28 12 17 , 6 3 2 1 2 10 23 2 18 , 1 6 2 2 19 , 13 4 2 3 4 3 5 2 2 8 16 4 15 20, 13 4 1 4 9 1 6 2 1 2 1 21, 2 1 1 2 1 1 1 22, 4 1 2 1 4 1 2 1 4 23, 13 1 1 2 7 3 1 24, x x x. ) 2 2 2 2 2 2 2 4 3 2 2 3 2 2 3 2 1 1 3 4 1 3 2 4 11 , 1 2 3 4 8 12 , 3 12 8 1 2 3 6 4 13 , 7 5 2 7 1 14, 4 3 4 1 2 3 1 3 1 7 1 15, 19 11 5 18 2 1 16, 13 53 39 5 4 15 2 5 1 17, 8 2 1 x x x x x x x x x x x. + ( ) 2 2 3 2 2 2 2 3 2 2 11 28 11 , 3 5 9 2 4 9 12 , 4 1 5 13 , 4 5 2 20 14 , 1 2 2 1 1 15 , 1 2 3 1 1 1 16, 2 1 1 3 8 17 , 5 4 1 1 18 , 5 4 19 , 4 3 4 20, 8 3 5 3 5 21, 1 2 1 1 22, 5 2 3 3 3 x x x x