Question

398. Решите уравнение: 1) (2x – 3) (4х + 3) – 8х2 = 33;
2) (2x – 6) (8х + 5) + (3 – 4x) (3 + 4x) = 55;
3) 21x2 - (3х - 7) (7x - 3) = 37;
4) (х + 1)(х + 2) - (х – 3)(х + 4) = 12;
5) (-4х + 1)(x-1) - х = (5 - 2x) (2x + 3) - 17​

Answer 1

$1) \: (2x - 3)(4x + 3) - 8 {x}^{2} = 33 \\ 8 {x}^{2} + 6x - 12x - 9 - 8 {x}^{2} = 33 \\ - 6x = 42 \\ x = - 7$

$2) \: (2x - 6)(8x + 5) + (3 - 4x)(3 + 4x) = 55 \\ 16 {x}^{2} + 10x - 48x - 30 + 9 - 16 {x}^{2} = 55 \\ - 38x = 76 \\ x = - 2$

$3) \: 21 {x}^{2} - (3x - 7)(7x - 3) = 37 \\ 21 {x}^{2} - (21 {x}^{2} - 9x - 49x + 21) = 37 \\ 9x + 49x - 21 = 37 \\ 58x = 58 \\ x = 1$

$4) \: (x + 1)(x + 2) - (x - 3)(x + 4) = 12 \\ {x}^{2} + 2x + x + 2 - ({x}^{2} + 4x - 3x - 12) = 12 \\ 3x + 2 - 4x + 3x + 12 = 12 \\ 2x = - 2 \\ x = - 1$

$5) \: ( - 4x + 1)(x - 1) - x = (5 - 2x)(2x + 3) - 17 \\ - 4 {x}^{2} + 4x + x - 1 - x = 10x + 15 - 4 {x}^{2} - 6x - 17 \\ - 4 {x}^{2} + 4x - 1 = - 4 {x}^{2} + 4x - 2 \\$