E3 f1 bộ binh
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Phương pháp đặt ẩn phụ phần 1.

Phương pháp đặt ẩn phụ phần 1.

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    E3 f1 bộ binh E3 f1 bộ binh Document Transcript

    • CHUYÊN ĐỀ PHƯƠNG TRÌNH – BẤT PHƯƠNG TRÌNH CHỨA CĂN THỨC PHƯƠNG PHÁP SỬ DỤNG ẨN PHỤ-------------------------------------------------------------------------------------------------------------------------------------------Bài 1. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, x − 3 + x = 9 29, 3 3 x 2 + x − 3x 2 − x = 2 2, 3 − x + x 2 − 2 x + x − x 2 = 1 30, 4 x 2 + x + 1 = 6 ( 4 x 2 + x ) + 13, x + 2 x + 5 < 4 2 x ( 2 + x ) + 3 2 31, x 2 − 4 x = −2 + x 2 + 5 − 4 x 4, x ( x − 4 ) 4 x − x + ( 2 − x ) < 2 2 2 32, ( 3 − x ) + 3x − 22 = x 2 − 3x + 7 25, ( x + 1) + ( x + 1) + 3x x + 1 > 0 2 3 33, x ( x + 5 ) > 2 3 x 2 + 5 x + 2 − 26, x 3 + x 2 − 1 + x 3 + x 2 + 2 = 3 34, 12 − 4 ( 4 − x )( x + 2 ) ≤ x 2 − 2 x7, 2 x 2 + 5 x + 2 − 2 2 x 2 + 5 x − 6 = 1 35, x 2 + 7 x + 4 = ( 4 x + 8 ) x8, 3 x + 21x + 18 + 2 x + 7 x + 7 = 2 2 2 36, x 2 − 7 x + 6 + x 2 − 7 x + 3 = 39, 3 x 2 + 6 x + 4 < 2 − 2 x − x 2 37, x 2 + x + 7 + x 2 + x + 2 = 3 x 2 + 3x + 1910, 4 x − 12 x − 5 4 x − 12 x + 11 + 15 = 0 2 2 38, 2 x 2 + x + 7 − 2 ( 2 x 2 + x + 1) = 3x 2 + ( x + 1) 211, x ( 2 x + 3) > 3 − 4 x − 6 x 2 39, 7 (1 + x )( 2 − x ) > 1 + 2 x − 2 x 212, 4 + ( x + 1)( 2 + x ) ≤ x 2 + 3 x 313, x 2 − 34 x + 48 ≥ 6 ( x − 2 )( x − 32 ) 40, x 2 + 3 − 2 x 2 − 3 x + 2 = x + 6 214, 9 x 2 + 3x + 12 = x ( x + 3) − 2 11 28 41, x 2 − 3 x − 5 9 x 2 + x − 2 = − x 4 915, 3 x 2 − 2 x + 15 = 7 − 3 x 2 − 2 x + 8 42, 4 x x + 1 + x + x = 5 3 216, 3 x + 5 x + 8 − 3 x + 5 x + 1 > 3 2 2 43, x x 2 + 4 + 5 ( x 2 + 2 ) = 20 217, 3 x 2 + 2 x = 2 x 2 + x + 1 − x 44, x 1 + x = 2 x 3 + 2 x − 118, 2 x + x 2 = 2 ( x 2 + 2 x + 4 ) + 3 1 x 45, 1 + + 2 =319, x + x + 2 = x ( x + 2 ) − 2 2 x x +1 x +1 x −120, 18 x 2 − 18 x + 5 = 3 3 9 x 2 − 9 x + 2 46, + =2 x −1 x +121, 3 3 x 3 − 3x + 2 = 2 x 2 − 6 x + 5 3+ x x +8 (22, 3 x − 2 x + 9 = 3 2 − 3x − 2 x + 1 2 2 ) 47, x + x =5 4x +1 123, 2 x ( x − 1) − x > x 2 − x + 1 48, + =5 4x x24, 3 x 2 + 15 x + 2 x 2 + 5 x + 1 = 2 49, x2 − 4 x + 3 = 4x − x225, ( x + 5 )( 2 − x ) = 3 x 2 + 3 x 50, 8 + x − 3 + 5 − x − 3 = 526, 5 x + 10 x + 1 > 7 − 2 x − x 2 2 51, 1 − x − x + 2 − x − x = 127, 2 x + x − 5 x − 6 = 10 x + 15 2 2 1 52, 5 + x + 2 3 − x > 3− x − 228, ( x + 1)( x + 4 ) ≤ 5 x + 2 x + 28 2 3CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 1
    • Bài 2. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, 4 x + 3 + 2 x + 1 = 6 x + 8 x 2 + 10 x + 3 − 16 12, 2 x + 1 + 9 − 2 x + 3 9 + 16 x − 4 x 2 > 13 25, x 2 + 2 x x − = 3x + 1 x 12 − x x − 2 823, (12 − x ) + ( x − 2) < 26, x 2 + 3 x 4 − x 2 = 1 + 2 x x−2 12 − x 3 1 3x 27, 1 − x 2 + 2 3 1 − x 2 = 34, > −1 3 1− x 2 1 − x2 28, 1 + x − x2 = x + 1 − x 2 7 5x5, ≤ +2 29, x + 7 + x + 2 x 2 + 7 x = 35 − 2 x 2− x 2 2 − x2 30, 2 x + 3 + 1 + x = 3 x + 2 2 x 2 + 5 x + 3 − 2 ( ) + 32 2 16, x + 16 + x = x + 16 + x 22 2 5 1 31, 5 x + > 2x + +4 1− x 8 2 + x 2 x 2x7, 8 + =2 2+ x 1− x 32, x −1 + x + 3 + 2 ( x − 1)( x + 3) + 2 x = 48, 3 2 + x − 6 2 − x + 4 4 − x 2 = 10 − 3 x 33, 3 x − 2 + x − 1 = 4 x − 9 + 2 3x 2 − 5 x + 2 x9, x + =2 2 34, 1 + x + 8 − x = 3 + (1 + x )( 8 − x ) x −1 2 2x 3 1 1 35, 3 + x + 6 − x = 3 + ( 3 + x )( 6 − x )10, 3 + + =2 x +1 2 2x 36, 3 x + 1 + 2 − x + 2 2 + 5 x − 3 x 2 = 9 − 2 x11, x + 4 + x − 4 = 2 x + 2 x 2 − 16 37, x + 2 − x 2 + x 2 − x 2 = 312, 4 x −1 + 4 x = 4 x + 1 38, x + 4 − x = 5 + 4 x − x2 x 3513, x + > 39, x+ 2 + 6− x = 8− ( x + 2 )( 6 − x ) x −1 2 12 (2 − x) + 3 ( 7 + x ) = 3 + 3 ( 7 + x )( 2 − x ) 3 2 2 40,14, x + 1 − 12 − x = − x 2 + 11x − 23 8− x15, 7 + x − 9 − x = − x 2 + 2 x + 63 41, 1 + x + 8 − x − (1 + x ) =3 1+ x16, 3 − x + x − 1 − 4 4 x − x 2 − 3 + 2 ≥ 0 42, 2 1 − 4 x + 5 x + 1 = (1 − 4 x )(1 + x ) + 517, 4 x − x −1 + x + x −1 = 2 2 2 x 2 − 6 x + 15 43, x 2 − 6 x + 18 =18, 9 ( x + 1) − x 2 = x + 9 − x x 2 − 6 x + 11 20 + x 20 − x x −119, − = 6 44, 1 − x + ( x − 1)( x − 2 ) + ( x − 2 ) =3 x x x−2 x−2 + x+2 x+220, x2 − 4 − x + 1 = 45, x 2 − 4 + 4 ( x − 2 ) = −3 2 x−2 8x221, x + 17 − x 2 + x 17 − x 2 = 9 46, 1 + 2 x − 1 − 2 x = 1 + 1 − 4 x222, x + 4 − x 2 = 2 + 3x 4 − x 2 2(2 − x) 2 1 1 47, x − 4− x =23, 1 − −2 +1 > 3 2 + 4 x − x2 x +1 x 424, x + = x − 2 +4 48, ( )( x + 3 − x −1 1 + x2 + 2 x − 3 = 4 ) x xCREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 2
    • Bài 3. Giải các phương trình và bất phương trình sau trên tập hợp số thực x +11, ( x − 3)( x + 1) + 4 ( x − 3) = −3 x−32, 2 1 − x − 1 + x + 3 1 − x 2 = 3 − x x+33, 2 x 2 − 9 = ( x + 5 ) x −3 x −14, 2 x 2 − 1 = x 2 + 2 x + 5 x +1 25, = 1 + 3 + 2x − x2 x +1 + 3 − x6, x 2 − x = ( 2 − 2 x ) x + 37, x 2 − 3 x + 6 = 2 ( 2 − x ) 3 + x8, 2 x 2 − 7 x + 15 = ( 9 − 4 x ) 3 + x9, x 2 − 1 = 2 x x 2 + 2 x10, x 2 + 4 x = ( x + 2 ) x 2 − 2 x + 411, x + 1 = x2 + 4 x + 512, 3 x = 3x 2 − 14 x + 1413, 7 x + 7 + 7 x − 6 + 2 49 x 2 + 7 x − 42 < 181 − 14 x14, ( 3 + x ) ( 4 − x )(12 + x ) + x = 28 2 x 2 − 3x + 515, = x2 + 2x −1 5 − 2x ( )16, 2 x 2 + 14 − 2 x 2 + 8 x x + 8 x − 14 x ( x + 8 ) + 24 = 017, x 2 − x − 2 1 + 16 x = 2 ( )(18, x + 15 x + 36 x + 5 x + 4 = 520 x ) x+419, 2 x 2 − 16 = ( 6 + x ) x−4  1 1 2 320,  x −  x 2 + 3x + = x  3 9 921, x 4 − 2 x 2 + x = 2 ( x 2 − x )22, 5 x 2 − 11x + 7 + ( 4 x − 5 ) x 2 − x + 1 = 0 5x2 − 9 x + 723, = x2 + x + 1 5 − 4x24, 5 x 2 − 11x + 7 = 2 ( 3 − 2 x ) x 2 + x + 2 125,5 16 − x 2 − =4 16 − x 2CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 3
    • Bài 4. Giải các phương trình và bất phương trình sau trên tập hợp số thực x2 + 21, ( x + 1) − 3x 2 <1 x2, ( x + 2 ) = 5 x 3 − 4 x + 8 23, x 2 + 5 x − 1 ≤ 6 x 3 − x4, 7 x ( x 2 + 3) + 6 ≥ ( x + 3) 2 2 ( 2 x 2 + x + 1)5, ≤ 2 x3 + x 56, 2 x 2 + 3 x + 4 − 5 x 3 + 2 x = 0 3 ( 4 x 2 + x + 1) 4x2 + 17, < 10 x x 3 ( x + 1) 2 x2 + x + 18, = 10 x x x2 + 19, 3 ( x + x + 3) = 10 ( 2 + x ) 2 x+2 10 x x − 110, 3 ( x 2 − x + 1) ≤ x11, ( x − 1) + x − x = 0 2 3 4 2 212, x 2 + 2 + x 3 x + = 2x x13, ( x − 1) + 3 x 2 ( x 2 − 2 ) = 3 2 x2 − 214, 3x 2 + 4 x − 6 > 7 x x x −115, x 2 + ( x + 1) ≤3 x +1 x2 − 316, 2 x 2 − 5 x − 3 x ≥6 x17, 6 x 2 − 3 3 x 2 − 2 x − 1 ≤ 4 x + 418, 2 ( 2 x 2 + 8 x + 6 ) = 4 + x ( ) 319, x −1 + 1 + 2 x −1 = 2 − x x +120, 2 x 2 − 8 x + 3 ( 5 − x ) = 12 x −521, 2 x 2 − 3 x + 1 ≥ 4 x − 4 x 2 − 3 x + 1 x 4 − 4 x 2 + 16 4 − x2 x22, ≤ + +1 x (4 − x ) 2 2 x 4 − x2CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 4
    • Bài 5. Giải các phương trình và bất phương trình sau trên tập hợp số thực x +11, 3 x + 5 < ( 3 x + 6 ) x+22, 3 ( x 2 − 3x + 9 ) < 2 x − 3 x − 63, 3 ( x 2 + 5 x + 9 ) ≤ 2 ( x + 3) + 5 x x− x4, ≥1 1 − 2 ( x − x + 1) 2 x −2 15, ≥ 6 ( x2 − 2 x + 4) − 2 x 2 3x − 4 x6, ≤1 5 ( x 2 + 13 x + 16 ) − 127, 3 x 2 + 12 x + 3 − x ≤ 1 − x x +18, ≤1 2 x + 5x + 1 + 3 x 29, ( x +1 )( x +3 ) >3 x 2 − 10 x + 910, 7 ( x − 1)( x − 4 ) ≤ x − x − 211, x 2 − 6 x + 1 ≥ (1 + x ) x12, 4 + x 2 = 5 x ( x − 2 ) 2 x+213, ≤ 3 x ( x + 1)( x + 4 ) 7 x 114, ≥ 4 x + 10 x + 1 x + 2 2 2 9 x2 − 5x + 115, . ≥ x 5 3x − 1 4x2 − 2x + 116, ≤ x 2x +117, 6 ( x 2 − 6 x + 4 ) + x ≤ 2 ( 2 + x )18, x 2 + 15 x + 9 ≤ 6 x ( 3 + x ) x3 − 7 x 2 − 819, ≥ 2x 3 x −720, ( x − 2 ) ≤ ( x 2 + 4 ) x 321, 2 + ( x − 2) ( 4 + x2 ) ≤ x + 2 x22, x 3 + 5 x 2 + ( x 2 − 10 x + 1) x ≤ 1 + 5 x 2CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 5
    • Bài 6. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, 6 x 2 − 7 x + 13 ≤ ( 7 − 6 x ) x 2 + 32, 15 x 2 − 7 x + 13 + (12 x − 7 ) x 2 + 3 = 0 18 x 2 − 7 x + 193, > 5 + 2 x2 7 − 12 x 18 x 2 + 15 x − 64, = 3x + 1 − 2 5 − 12 x5, 8 x 2 − 9 x + 8 + ( 8 x − 5 ) 1 + 3 x = 06, ( x + 1) + 2 ( 3 − x ) 2 x + 1 = 6 x − 5 2 2 x2 − 5x + 4 2 ( x + 1)7, −1 = 2x − 3 2x + 3 +18, 2 + x ( 3 x − 5 ) + ( 3 x − 5 ) x 2 − 1 = 09, 4 (1 + x ) = ( 2 x + 1) 2 x + 110, x + 4 + x 2 − x + 4 = 3 x 211, 7 x 2 − 2 x = 1 + 2 x 2 − x + 112, 7 x ( 2 x − 1) ≤ 2 x ( 2 x + 1) 3 213, x + 4 x2 + x − 7 = x + 7 414, 3x 2 − 28 + 8 x 2 + x − 7 = 015, 23 x 2 − 32 x = 4 x 3x 2 + 5 x + 2 + 716, 2 x 2 + x − 4 = 2 2 x 2 + 3 x + 4 2 x − 1 − 28 x 217, 3 x 2 + 1 < 24 x − 1 x 2 2 − x − 6 x218, = 1 + 1 + 5x2 5 ( 2 x − 1) 5 1319, 3x 2 + x + + 2 x 2 x 2 + x + 5 = 0 2 4 2 x2 − 5x + 7 + 2 x2 + 2 x − 320, ≤ 9 − 2x x2 + 2x − 3 x 2 + x + 10 3 ( 2 − x )21, ≥ −1 4 x 2 − 5 x + 26 5 − 2x 5 x + 1722, > x+5 − x 16 x + 1 2 − x 2 (1 + x )( x − 4 )23, ≤ 11 − 2 x x − 3x + 4 x +3 224, 4− x ( = 4 x + 1 −1 )CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 6
    • Bài 7. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, 2 ( 2 − x ) + 7 x 3 − 4 x ≤ 16 22, 4 x 4 − 8 x 2 + 7 2 x 4 − x 2 > 23, 2 x 2 + 7 x + 1 + x + 1 ≤ 3 x 3 x2 + 6x + 1 + x4, ≥1 5 x −1 4 x2 + x + 1 − 3 x + 35, ≤ −1 x−2 3 x2 − 5x + 4 − 5 x + 36, ≤1 1− x 4 x + 7 x − 167, ≥6 ( x + 1)( x + 4 ) + x − 2 ( x + 1) + 3 ≤ 2 + x 28, x2 + 3x + 4 + x 15 + ( 2 x − 1) 29, x 2 + 3x + 4 − 2 x ≥4 ( x +1 )( x +2 ) 2 (1 + x ) 2 (10, 2 x + 1 )( x +2 ≤ ) x2 + 3x + 1 − x 2 4 x 2 − 3x + 1 − 5 x − 411, ≤1 2x − 3 7 4 x 2 − 5 x + 1 − x + 1512, =2 7−x13, 6 x 2 + 24 x + 26 ≤ x (1 − x )14, 6 x 2 + 24 x + 26 = ( 7 − x ) x  4 15, ( 3 − x ) ≥ 6 +  3 x − + 8  2 x − 1 2  x   416, ( x − 6 ) < 16 + 3x −  4 x − 1 + 33 2  x  36 17, 11x 2 + 19 x −  4 x 2 − 9 = 27 x  x  3 118, 2 x 2 − 9 x + 3 = 10 ( 3 x − 1)− x x2  1 1 319,  2 −  2 x − 1 ≤ ( x − 3) + 2  x 5 2 1 20, 14 x 2 < 3 + 10  − 4 x  1 − 4 x 2 x  x 2 − 3 x − 6 10 x 2 − x − 221, < 2 + x − x2 xCREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 7
    • Bài 8. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, x 3 + 12 x ≤ 18 x 2 + 9 ( 3 x − 2 ) 3 x − 22, x ( x − 3) + 21x + 9 ( 5 − x ) x − 5 = 0 23, 7 x 2 − 6 ≥ 9 x (1 − x 2 ) 1 − x 24, x ( 6 − 25 x 2 ) + 9 ( 9 − 4 x 2 ) 9 − 4 x 2 = 0 1 − x 2x −15, ≤ 1− 2x 2 x −1 x ( x − 1)( 2 − x )6, ≥ 2 2 − 3x 3x − 2  8 7, x 2 +  x − + 36  2 x − 9 + 4 x ≤ 18  x 8, x 3 + ( x 2 − 16 x + 12 ) 4 x − 3 + 8 x 2 = 6 x x −19, ( x + 1) + .( x − 2) ≥ 3 2 2 x x 2 + x + 1 3 x + 2 ( x + 1) 210, ≥ 2 x 3 x + 4 ( x + 1) x ( 3x2 + 2 x − 4)11, = ( x − 1)( x + 2 ) 3x 2 + 4 x − 812, ( 3x 2 + 12 x + 8 ) (1 + x )( 2 + x ) ≤ x ( 3x 2 + 6 x + 4 )13, 7 x 2 + 5 2 x + 7 = x 4 + 114, 4 x 3 + 3 x 2 + 4 x + 1 = 2 ( 3 x + 1) 3 x + 1 7  1 15, x 2 + 19 x + 11 ≤ +  5 x + + 18  2 x − 1 x  x 16, x 3 + 13 x 2 − 53x + 39 ≤ ( 5 x 2 − 4 x − 15 ) 2 x − 5  117,  8 x − 2 +  1 − 2 x ≥ 4 x 2 − 10 x + 5  x18, ( x − 3) + ( 2 x − 7 ) x − 3 = 0 219, 2 x + 1 + 3 x − 2 = 2 x 2 − x − 2 + 3 1 + x20, 5 x + 10 x − 2 = 2 + 4 x 2 − 4 + 5 2 + x21, 12 x − 1 + 13x < 2 + 12 x 2 − 1 + 8 x + 122, 10 x − 4 + 8 x 2 − 1 = 5 1 + x + 10 x − 1 12 6 23, 2 x + = 5 +  − 2  x2 + x + 7 x x  x 4 + 2 x3 − x 2 − 2 x + 324, = x2 + x + 1 2x + 2x − 3 2CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 8
    • Bài 9. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, x + 7 + 2 ( 3 x − 2 )( 3 − 2 x ) = 5 3x − 2 + 5 3 − 2 x2, 11 − 3 x + 10 1 − x = 5 x + 1 + 4 1 − x 23, ( x − 2 )( x − 7 ) = 2 − 2x 5 − 2x 3 − 2x −1 ( )4, ( x 2 + 5 x + 12 ) 1 − 1 − 2 x = 4 x 2 + 10 x 2 ( x + 3)( 2 x + 3)5, 2 − 1 − 2 x ≤ x2 + 8x + 2 x 2 − x + 28 9 − 2x6, = 3x 1 + 3x − 1 x − 7 x + 55 2 37, ≥ ( 9 − 2 x )( 5 − x ) 4 − 1 + 3x8, 5 x + 17 + 14 x + 1 = 6 x 2 + 4 x + 3 + 7 3 − x x3 + 3x 2 − 4 x + 69, = 1+ x 6 − x − 3x 210, x 3 + 3 x 2 − x + 6 ≤ ( 3 x 2 + x − 5 ) 2 + x11, ( 3 x 2 + 2 x − 7 ) 1 + 2 x + x 3 + 6 x 2 − 5 x + 12 > 0 1012, x 2 + x ≤ ( x − 1) x − 1 + 1 x x3 + 3x 2 − 3x13, 10 3x − 1 ≥ 3x − 1 x + 25 x − 68 x + 12 3 2 5 ( x − 2)14, = 5 x + 20 x − 4 2 5x −1 + 3 x 3 + 44 x 2 − 33 x15, ≤ ( x 2 + 4 x − 3) 4 x − 3 6 2 x 3 + 22 x − 11x 116, >6 x− 2x + 2x −1 2 2 x + 5 x − 28 x + 12 3 217, 6 ( x − 3) ≤ x2 + x − 2 ( x − 2 +1 ) x 3 + 10 x 2 − 23 x + 218, 1 + =6 x−2 x2 + x − 219, (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 = 122, ( 4 x − 1) 2 x − 1 + ( 4 x + 1) 2 x + 1 = 423, (13x + 1) 1 + x = 2 ( 7 x + 3) x + 124, 8 x = 19 + x 3 + 6 x x + 1CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 9
    • Bài 10. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, 8 x 3 + 8 = ( 2 x + 3 − 12 x 2 ) 2 x + 3 + 12 x 2 + 18 x2, ( 3x 2 + 9 x + 5 ) 3 x + 2 + x 3 + 12 x 2 + 18 x = 13, x 3 + 12 x 2 + ( 6 x 2 + 8 x − 24 ) x − 3 = 1 + 36 x4, 9 ( x 2 + 3 x + 6 ) x + 2 = 27 ( x + 1) + x 3 2 x 3 + 12 x 2 + 24 x + 275, 2 2 + x ≥ 3x 2 + 4 x + 8 8 x 3 + 6 x ( x + 5 ) + 276, 5 x + 5 < 12 x 2 + x + 57, x 3 + 3 x 2 + 3 x = ( 3 x + 4 ) x + 78, x 3 + 6 x 2 + 12 x + ( 4 x + 2 ) x = 209, 7 x 3 + 3 x 2 + (12 x 2 + x ) x = 1 + 3 x 3 910, 3x x − 5 x + + x2 = x x  3  2611, x 2 + 15 ( x + 1) + 2 x  3x + 10 +  ≤  x x 3 3x12, +1 < 3− x 2 3 − x2 9 − 4x 3 − 2x13, + ≥2 2 − x2 2 − x2 5x 2 + 3x + 114, ≥5 ( x + 1) ( x3 − 1) 6 x2 − 815, +1 ≥ x 4 − x (6 − x) 4 5x16, > +9 2 − x3 x3 − 2 3 2 − x3 12 x17, + 14 ≤ 1− x 3 3 1 − x3 1 18, x 2 + 12 x + 16  − 1 1 − x ≤ 12 x 19, 16 x 3 < (11x 2 − x + 2 ) ( x − 1)( 2 + x ) 11 1 + x 2 1620, ≤ ( x + 1) 3 24 x2 + x +1 1121, (12 x 2 − 25 x + 12 ) 1 + x + 16 (1 − x ) = 0 3 6 x3 − 5 x22, ≤ 2 x2 −1 3x 2 − 1CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 10
    • Bài 11. Giải các phương trình và bất phương trình sau trên tập hợp số thực1, x 2 + 4 x + 9 > 7 x ( x − 3) x 2 − x + 232, > 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 + 8x5, ≥ 9 x +1 x −1 1  16, x + 14 + = 10 1 −  x x  x7, ( 4 + x ) + 10 ( 4 − x ) x ≥ 0 2 (8, x 2 + 11x < 3 3 x + 1 ( x − 3) ) 2 x 2 + 3x + 2 + x − 29, ≤1 2 x −3 2x2 + 7 x + 8 + 210, >1 2 x−x 2 x 2 + 10 x + 811, ≤1 x−3 x + 212, x + 3 ≤ 3 x + 2 ( x 2 + 7 x − 9 )13, x 2 + 3x + 2 + x 2 + 3x ≥ 4 214, x 2 + 12 x + 2 ≥ 7 x x + x x2 −115, x 2 + 15 x − 8 x ≥1 x 1 − 2 x216, 1 − 3 x ≤ 2 x 2 + 10 x x 3 − 4 x217, 3 > 5 x + 14 x + 4 x 2 x18, ( 3 x 2 − 3x − 1) 3x − 1 + 2x ≤ 0 x 1 2x19, 4 x − ≥ x 3x + 1 − 4 x220, x + 3 ≥ 6 x − 4 x 2 − 29 x + 3621, ( x 2 + 2 − 8 x ) x + 2 + 12 x ≤ x 2 + 2 x x2 + 9x + 4 422, 2 x+ ≥2 3 x + 2 x + 12 xCREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH 11