Вариант 4 • 1. Решите уравнение: a) 9x27x-2 = 0; в) 5х2 = 45; б) 4x2 - x = 0; г) х² + 18x - 63 = 0.

Решим уравнения.

1. a) $$9x^2 - 7x - 2 = 0$$
   $$D = (-7)^2 - 4 \cdot 9 \cdot (-2) = 49 + 72 = 121$$
   $$x_1 = \frac{7 + \sqrt{121}}{2 \cdot 9} = \frac{7 + 11}{18} = \frac{18}{18} = 1$$
   $$x_2 = \frac{7 - \sqrt{121}}{2 \cdot 9} = \frac{7 - 11}{18} = \frac{-4}{18} = -\frac{2}{9}$$
2. б) $$4x^2 - x = 0$$
   $$x(4x - 1) = 0$$
   $$x_1 = 0, x_2 = \frac{1}{4} = 0.25$$
3. в) $$5x^2 = 45$$
   $$x^2 = \frac{45}{5} = 9$$
   $$x_1 = 3, x_2 = -3$$
4. г) $$x^2 + 18x - 63 = 0$$
   $$D = 18^2 - 4 \cdot 1 \cdot (-63) = 324 + 252 = 576$$
   $$x_1 = \frac{-18 + \sqrt{576}}{2 \cdot 1} = \frac{-18 + 24}{2} = \frac{6}{2} = 3$$
   $$x_2 = \frac{-18 - \sqrt{576}}{2 \cdot 1} = \frac{-18 - 24}{2} = \frac{-42}{2} = -21$$

Ответ: a) $$x_1 = 1, x_2 = -\frac{2}{9}$$, б) $$x_1 = 0, x_2 = 0.25$$, в) $$x_1 = 3, x_2 = -3$$, г) $$x_1 = 3, x_2 = -21$$