Вариант 3 • 1. Решите уравнение: a) 7x29x + 2 = 0; в) 7х2-28 = 0; 6) 5x2 = 12x; г) х² + 20x + 91 = 0.

Решим уравнения.

1. a) $$7x^2 - 9x + 2 = 0$$
   
   $$D = (-9)^2 - 4 \cdot 7 \cdot 2 = 81 - 56 = 25$$
   
   $$x_1 = \frac{9 + \sqrt{25}}{2 \cdot 7} = \frac{9 + 5}{14} = \frac{14}{14} = 1$$
   
   $$x_2 = \frac{9 - \sqrt{25}}{2 \cdot 7} = \frac{9 - 5}{14} = \frac{4}{14} = \frac{2}{7}$$


2. б) $$5x^2 = 12x$$
   
   $$5x^2 - 12x = 0$$
   
   $$x(5x - 12) = 0$$
   
   $$x_1 = 0, x_2 = \frac{12}{5} = 2.4$$


3. в) $$7x^2 - 28 = 0$$
   
   $$7x^2 = 28$$
   
   $$x^2 = 4$$
   
   $$x_1 = 2, x_2 = -2$$


4. г) $$x^2 + 20x + 91 = 0$$
   
   $$D = 20^2 - 4 \cdot 1 \cdot 91 = 400 - 364 = 36$$
   
   $$x_1 = \frac{-20 + \sqrt{36}}{2 \cdot 1} = \frac{-20 + 6}{2} = \frac{-14}{2} = -7$$
   
   $$x_2 = \frac{-20 - \sqrt{36}}{2 \cdot 1} = \frac{-20 - 6}{2} = \frac{-26}{2} = -13$$

Ответ: a) $$x_1 = 1, x_2 = \frac{2}{7}$$, б) $$x_1 = 0, x_2 = 2.4$$, в) $$x_1 = 2, x_2 = -2$$, г) $$x_1 = -7, x_2 = -13$$