Вариант 2 Тип 1 1. (2x-5)(2x + 5) = 0 2. 3(x² - 4) = 0 3. 6x2 = 54 4. \frac{x²}{4}-9=0 5. -4x²+36= 0 Тип 2 6. x(x - 8) = 0 7. 2x2 = -10x 8. \frac{x²}{3}+ 5x = 0 9. -3x² + 12x = 0 10. 4x2 = 20x

Решение заданий:

Тип 1

1. \[(2x - 5)(2x + 5) = 0\] Используем формулу разности квадратов: \[a^2 - b^2 = (a - b)(a + b)\] \[4x^2 - 25 = 0\] \[4x^2 = 25\] \[x^2 = \frac{25}{4}\] \[x = \pm \frac{5}{2}\] \[x_1 = 2.5, x_2 = -2.5\]
2. \[3(x^2 - 4) = 0\] \[x^2 - 4 = 0\] \[x^2 = 4\] \[x = \pm 2\] \[x_1 = 2, x_2 = -2\]
3. \[6x^2 = 54\] \[x^2 = \frac{54}{6}\] \[x^2 = 9\] \[x = \pm 3\] \[x_1 = 3, x_2 = -3\]
4. \[\frac{x^2}{4} - 9 = 0\] \[\frac{x^2}{4} = 9\] \[x^2 = 36\] \[x = \pm 6\] \[x_1 = 6, x_2 = -6\]
5. \[-4x^2 + 36 = 0\] \[4x^2 = 36\] \[x^2 = 9\] \[x = \pm 3\] \[x_1 = 3, x_2 = -3\]

Тип 2

1. \[x(x - 8) = 0\] \[x = 0 \quad \text{или} \quad x - 8 = 0\] \[x_1 = 0, x_2 = 8\]
2. \[2x^2 = -10x\] \[2x^2 + 10x = 0\] \[2x(x + 5) = 0\] \[x = 0 \quad \text{или} \quad x + 5 = 0\] \[x_1 = 0, x_2 = -5\]
3. \[\frac{x^2}{3} + 5x = 0\] Умножим обе части на 3: \[x^2 + 15x = 0\] \[x(x + 15) = 0\] \[x = 0 \quad \text{или} \quad x + 15 = 0\] \[x_1 = 0, x_2 = -15\]
4. \[-3x^2 + 12x = 0\] \[-3x(x - 4) = 0\] \[x = 0 \quad \text{или} \quad x - 4 = 0\] \[x_1 = 0, x_2 = 4\]
5. \[4x^2 = 20x\] \[4x^2 - 20x = 0\] \[4x(x - 5) = 0\] \[x = 0 \quad \text{или} \quad x - 5 = 0\] \[x_1 = 0, x_2 = 5\]

Ответ: Решения уравнений выше.

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