1) 100x² - 16 = 100x² = 1x² = 16/10x² = 0.1x = ±√0.1x = ±0.4
Ответ: x₁ = 0.4, x₂ = -0.4
2) 4x² - 7x - 2 = 4x² - 8x + x - 2 = 4x(x-2) + 1(x-2) = (4x+1)(x-2) = 4x+1 = 0 => x = -1/x-2 = 0 => x = 2
Ответ: x₁ = -1/4, x₂ = 2
3) 3x² + 8x - 3 = 3x² + 9x - x - 3 = 3x(x+3) - 1(x+3) = (3x-1)(x+3) = 3x-1 = 0 => x = 1/x+3 = 0 => x = -3
Ответ: x₁ = 1/3, x₂ = -3
4) (2x-3)² = 11x-14x² - 12x + 9 = 11x - 14x² - 23x + 28 = 4x² - 16x - 7x + 28 = 4x(x-4) - 7(x-4) = (4x-7)(x-4) = 4x-7 = 0 => x = 7/x-4 = 0 => x = 4
Ответ: x₁ = 7/4, x₂ = 4
1) 100x² - 16 =
100x² = 1
x² = 16/10
x² = 0.1
x = ±√0.1
x = ±0.4
Ответ: x₁ = 0.4, x₂ = -0.4
2) 4x² - 7x - 2 =
4x² - 8x + x - 2 =
4x(x-2) + 1(x-2) =
(4x+1)(x-2) =
4x+1 = 0 => x = -1/
x-2 = 0 => x = 2
Ответ: x₁ = -1/4, x₂ = 2
3) 3x² + 8x - 3 =
3x² + 9x - x - 3 =
3x(x+3) - 1(x+3) =
(3x-1)(x+3) =
3x-1 = 0 => x = 1/
x+3 = 0 => x = -3
Ответ: x₁ = 1/3, x₂ = -3
4) (2x-3)² = 11x-1
4x² - 12x + 9 = 11x - 1
4x² - 23x + 28 =
4x² - 16x - 7x + 28 =
4x(x-4) - 7(x-4) =
(4x-7)(x-4) =
4x-7 = 0 => x = 7/
x-4 = 0 => x = 4
Ответ: x₁ = 7/4, x₂ = 4