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

Решим уравнения.

1. a) $$2x^2+7x-9=0$$
   $$D = 7^2 - 4 \cdot 2 \cdot (-9) = 49 + 72 = 121$$
   $$x_1 = \frac{-7 + \sqrt{121}}{2 \cdot 2} = \frac{-7 + 11}{4} = \frac{4}{4} = 1$$
   $$x_2 = \frac{-7 - \sqrt{121}}{2 \cdot 2} = \frac{-7 - 11}{4} = \frac{-18}{4} = -4.5$$
2. б) $$3x^2=18x$$
   $$3x^2 - 18x = 0$$
   $$3x(x - 6) = 0$$
   $$x_1 = 0, x_2 = 6$$
3. в) $$100x^2 - 16 = 0$$
   $$100x^2 = 16$$
   $$x^2 = \frac{16}{100} = \frac{4}{25}$$
   $$x_1 = \frac{2}{5} = 0.4, x_2 = -\frac{2}{5} = -0.4$$
4. г) $$x^2 - 16x + 63 = 0$$
   $$D = (-16)^2 - 4 \cdot 1 \cdot 63 = 256 - 252 = 4$$
   $$x_1 = \frac{16 + \sqrt{4}}{2 \cdot 1} = \frac{16 + 2}{2} = \frac{18}{2} = 9$$
   $$x_2 = \frac{16 - \sqrt{4}}{2 \cdot 1} = \frac{16 - 2}{2} = \frac{14}{2} = 7$$

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) $$x_1 = 9, x_2 = 7$$