• 1. Решите уравнение: a) 7x²-9x+2=0; б) 5x2=12x; в) 7х2-28=0; г) х²+20х+91=0.

Решим уравнения: a) \(7x^2 - 9x + 2 = 0\) Дискриминант \(D = (-9)^2 - 4 \times 7 \times 2 = 81 - 56 = 25\) \(x_1 = \frac{9 + \sqrt{25}}{2 \times 7} = \frac{9 + 5}{14} = \frac{14}{14} = 1\) \(x_2 = \frac{9 - \sqrt{25}}{2 \times 7} = \frac{9 - 5}{14} = \frac{4}{14} = \frac{2}{7}\) б) \(5x^2 = 12x\) \(5x^2 - 12x = 0\) \(x(5x - 12) = 0\) \(x_1 = 0\) \(5x - 12 = 0\) \(5x = 12\) \(x_2 = \frac{12}{5} = 2.4\) в) \(7x^2 - 28 = 0\) \(7x^2 = 28\) \(x^2 = \frac{28}{7} = 4\) \(x = \pm \sqrt{4}\) \(x_1 = 2, x_2 = -2\) г) \(x^2 + 20x + 91 = 0\) Дискриминант \(D = 20^2 - 4 \times 1 \times 91 = 400 - 364 = 36\) \(x_1 = \frac{-20 + \sqrt{36}}{2 \times 1} = \frac{-20 + 6}{2} = \frac{-14}{2} = -7\) \(x_2 = \frac{-20 - \sqrt{36}}{2 \times 1} = \frac{-20 - 6}{2} = \frac{-26}{2} = -13\) Ответ: а) \(x_1 = 1\), \(x_2 = \frac{2}{7}\); б) \(x_1 = 0\), \(x_2 = 2.4\); в) \(x_1 = 2\), \(x_2 = -2\); г) \(x_1 = -7\), \(x_2 = -13\)