Question

3.Решите уравнение: 1)(7x+1)(x-3)+20(x-1)(x+1)=3(3x-2)²+13 2)(3x+5)²-64=0 3)(3z+5)²-(4z-7)²=0 4)(x+4)²+(x-8)²=2(8-x)(x+4)

Answer 1

В 1 номере там,где жироно выделены цифры,это 3×4
Если что-то непонятно-обращайся^^

Answer 2

1) (7x+1)(x-3) + 20(x-1)(x+1) = 3(3x-2)² + 13 Expand the expressions: 7x^2 - 21x + x - 3 + 20(x^2 - 1) = 9x^2 - 12x + 4 + 13 7x^2 - 20x - 3 + 20x^2 - 20 = 9x^2 - 12x + 17 27x^2 - 20x - 23 = 9x^2 - 12x + 17 Subtract 9x^2 - 12x + 17 from both sides: 18x^2 + 8x - 40 = 0 Factor the quadratic equation: 2(9x^2 + 4x - 20) = 0 2(3x+5)(3x-4) = 0 3x+5 = 0 or 3x-4 = 0 x = -5/3 or x = 4/3

2) (3x+5)² - 64 = 0 Expand the expression: 9x^2 + 30x + 25 - 64 = 0 9x^2 + 30x - 39 = 0 Divide by 3: 3x^2 + 10x - 13 = 0 Use the quadratic formula to solve for x: x = (-10 ± √(10^2 - 4*3*(-13))) / (2*3) x = (-10 ± √(100 + 156)) / 6 x = (-10 ± √256) / 6 x = (-10 ± 16) / 6 x = (-10 + 16) / 6 or x = (-10 - 16) / 6 x = 1 or x = -9/3 x = 1 or x = -3

3) (3z+5)² - (4z-7)² = 0 Expand the expressions: 9z^2 + 30z + 25 - 16z^2 + 56z - 49 = 0 -7z^2 + 86z - 24 = 0 Divide by -1: 7z^2 - 86z + 24 = 0 Use the quadratic formula to solve for z: z = (86 ± √((-86)^2 - 4*7*24)) / (2*7) z = (86 ± √(7396 - 672)) / 14 z = (86 ± √6724) / 14 z = (86 ± 82) / 14 z = (86 + 82) / 14 or z = (86 - 82) / 14 z = 168 / 14 or z = 4 / 14 z = 12 or z = 2/7

4) (x+4)² + (x-8)² = 2(8-x)(x+4) Expand the expressions: x^2 + 8x + 16 + x^2 - 16x + 64 = 16x - 2x^2 - 64 2x^2 - 8x + 80 = 0 Divide by 2: x^2 - 4x + 40 = 0 Use the quadratic formula to solve for x: x = (4 ± √((-4)^2 - 4*1*40)) / (2*1) x = (4 ± √(16 - 160)) / 2 x = (4 ± √(-144)) / 2 Since the discriminant is negative, the solutions are complex numbers.