Вариант 1 • 1. Решите уравнение: a) 2x² + 7x9=0; B) 100x²-16=0; 6) 3x² = 18x; г) х²-16х +63-0.

Вариант 1

1. Решите уравнение:

а) $$2x^2 + 7x - 9 = 0$$ $$D = b^2 - 4ac = 7^2 - 4 \cdot 2 \cdot (-9) = 49 + 72 = 121$$ $$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-7 + \sqrt{121}}{2 \cdot 2} = \frac{-7 + 11}{4} = \frac{4}{4} = 1$$ $$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-7 - \sqrt{121}}{2 \cdot 2} = \frac{-7 - 11}{4} = \frac{-18}{4} = -4.5$$
б) $$3x^2 = 18x$$ $$3x^2 - 18x = 0$$ $$3x(x - 6) = 0$$ $$x_1 = 0$$ $$x - 6 = 0$$ $$x_2 = 6$$
в) $$100x^2 - 16 = 0$$ $$100x^2 = 16$$ $$x^2 = \frac{16}{100}$$ $$x^2 = 0.16$$ $$x_1 = \sqrt{0.16} = 0.4$$ $$x_2 = -\sqrt{0.16} = -0.4$$
г) $$x^2 - 16x + 63 = 0$$ $$D = b^2 - 4ac = (-16)^2 - 4 \cdot 1 \cdot 63 = 256 - 252 = 4$$ $$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{16 + \sqrt{4}}{2 \cdot 1} = \frac{16 + 2}{2} = \frac{18}{2} = 9$$ $$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{16 - \sqrt{4}}{2 \cdot 1} = \frac{16 - 2}{2} = \frac{14}{2} = 7$$
Ответ: а) $$x_1 = 1, x_2 = -4.5$$; б) $$x_1 = 0, x_2 = 6$$; в) $$x_1 = 0.4, x_2 = -0.4$$; г) $$x_1 = 9, x_2 = 7$$