Вариант 1 • 1. Решите уравнение: a) 2x²+7x- 9 = 0; в) 100х2-16 = 0; 6) 3x² = 18x; г) x² - 16x + 63 = 0.

a) $$2x^2 + 7x - 9 = 0$$

Найдем дискриминант:

$$D = b^2 - 4ac = 7^2 - 4 \cdot 2 \cdot (-9) = 49 + 72 = 121$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-7 + \sqrt{121}}{2 \cdot 2} = \frac{-7 + 11}{4} = \frac{4}{4} = 1$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-7 - \sqrt{121}}{2 \cdot 2} = \frac{-7 - 11}{4} = \frac{-18}{4} = -4.5$$

б) $$3x^2 = 18x$$

$$3x^2 - 18x = 0$$

Вынесем х за скобки:

$$x(3x - 18) = 0$$

$$x_1 = 0$$

$$3x - 18 = 0$$

$$3x = 18$$

$$x_2 = \frac{18}{3} = 6$$

в) $$100x^2 - 16 = 0$$

$$(10x - 4)(10x + 4) = 0$$

$$10x - 4 = 0$$

$$10x = 4$$

$$x_1 = \frac{4}{10} = 0.4$$

$$10x + 4 = 0$$

$$10x = -4$$

$$x_2 = -\frac{4}{10} = -0.4$$

г) $$x^2 - 16x + 63 = 0$$

Найдем дискриминант:

$$D = b^2 - 4ac = (-16)^2 - 4 \cdot 1 \cdot 63 = 256 - 252 = 4$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{16 + \sqrt{4}}{2 \cdot 1} = \frac{16 + 2}{2} = \frac{18}{2} = 9$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{16 - \sqrt{4}}{2 \cdot 1} = \frac{16 - 2}{2} = \frac{14}{2} = 7$$

Ответ: a) $$x_1 = 1$$, $$x_2 = -4.5$$; б) $$x_1 = 0$$, $$x_2 = 6$$; в) $$x_1 = 0.4$$, $$x_2 = -0.4$$; г) $$x_1 = 9$$, $$x_2 = 7$$