697. Решите уравнение: 1) x² - 3x + 2 = 0; 2) x² + 12x - 13 = 0; 3) x² - 7x + 10 = 0; 4) x²-x - 72 = 0; 5) 2x² - 5x + 2 = 0; 6) 2x² - 7x-4 = 0; 7) 4x² - 3x - 1 = 0; 8) −2x² + x + 15 = 0;

Решение уравнений:

1) \(x^2 - 3x + 2 = 0\) Дискриминант: \(D = (-3)^2 - 4 \cdot 1 \cdot 2 = 9 - 8 = 1\) Корни: \(x_1 = \frac{3 + \sqrt{1}}{2} = \frac{3 + 1}{2} = 2\), \(x_2 = \frac{3 - \sqrt{1}}{2} = \frac{3 - 1}{2} = 1\) 2) \(x^2 + 12x - 13 = 0\) Дискриминант: \(D = 12^2 - 4 \cdot 1 \cdot (-13) = 144 + 52 = 196\) Корни: \(x_1 = \frac{-12 + \sqrt{196}}{2} = \frac{-12 + 14}{2} = 1\), \(x_2 = \frac{-12 - \sqrt{196}}{2} = \frac{-12 - 14}{2} = -13\) 3) \(x^2 - 7x + 10 = 0\) Дискриминант: \(D = (-7)^2 - 4 \cdot 1 \cdot 10 = 49 - 40 = 9\) Корни: \(x_1 = \frac{7 + \sqrt{9}}{2} = \frac{7 + 3}{2} = 5\), \(x_2 = \frac{7 - \sqrt{9}}{2} = \frac{7 - 3}{2} = 2\) 4) \(x^2 - x - 72 = 0\) Дискриминант: \(D = (-1)^2 - 4 \cdot 1 \cdot (-72) = 1 + 288 = 289\) Корни: \(x_1 = \frac{1 + \sqrt{289}}{2} = \frac{1 + 17}{2} = 9\), \(x_2 = \frac{1 - \sqrt{289}}{2} = \frac{1 - 17}{2} = -8\) 5) \(2x^2 - 5x + 2 = 0\) Дискриминант: \(D = (-5)^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9\) Корни: \(x_1 = \frac{5 + \sqrt{9}}{4} = \frac{5 + 3}{4} = 2\), \(x_2 = \frac{5 - \sqrt{9}}{4} = \frac{5 - 3}{4} = \frac{1}{2}\) 6) \(2x^2 - 7x - 4 = 0\) Дискриминант: \(D = (-7)^2 - 4 \cdot 2 \cdot (-4) = 49 + 32 = 81\) Корни: \(x_1 = \frac{7 + \sqrt{81}}{4} = \frac{7 + 9}{4} = 4\), \(x_2 = \frac{7 - \sqrt{81}}{4} = \frac{7 - 9}{4} = -\frac{1}{2}\) 7) \(4x^2 - 3x - 1 = 0\) Дискриминант: \(D = (-3)^2 - 4 \cdot 4 \cdot (-1) = 9 + 16 = 25\) Корни: \(x_1 = \frac{3 + \sqrt{25}}{8} = \frac{3 + 5}{8} = 1\), \(x_2 = \frac{3 - \sqrt{25}}{8} = \frac{3 - 5}{8} = -\frac{1}{4}\) 8) \(-2x^2 + x + 15 = 0\) Дискриминант: \(D = 1^2 - 4 \cdot (-2) \cdot 15 = 1 + 120 = 121\) Корни: \(x_1 = \frac{-1 + \sqrt{121}}{-4} = \frac{-1 + 11}{-4} = -\frac{5}{2}\), \(x_2 = \frac{-1 - \sqrt{121}}{-4} = \frac{-1 - 11}{-4} = 3\)

Ответ: См. решение