1) (7x + 1)(x - 3) + 20(x - 1)(x + 1) = 3(3x - 2)² + 13
7x² - 21x + x - 3 + 20x² - 20 = 3(9x² - 12x + 4) + 13
27x²- 20x - 23 - 27x² + 36x - 12 - 13 = 0
16x - 48 = 0
16x = 48
x = 3
2) (3x + 5)² - 64 = 0
(3x + 5)² - 8² = 0
(3x + 5 - 8)(3x + 5 + 8) = 0
(3x - 3)(3x + 13) = 0
или 3x - 3 = 0 или 3x + 13 = 0
3x = 3 3x = - 13
x₁ = 1 x₂ = - 4 1/3
3) (3z + 5)² - (4z - 7)² = 0
(3z + 5 - 4z + 7)(3z + 5 + 4z - 7) = 0
(- z + 12)(7z - 2) = 0
или - z + 12 = 0 или 7z - 2 = 0
z₁ = 12 z₂ = 2/7
4) (x + 4)² + (x - 8)² = 2(8 - x)(x + 4)
(x + 4)² - 2(8 - x)(x + 4) + (8 - x)² = 0
(x + 4 - 8 + x)² = 0
(2x - 4)² = 0
2x - 4 = 0
2x = 4
x = 2
4) x² + 4x + 7 = 0
D = 4² - 4 * 7 = 16 - 28 = - 12 < 0
Дискриминант меньше нуля, значит уравнение не имеет корней.