5 Решите уравнение: a) (2x - 5)² - (2x - 3)(2x + 3) = 0; б) 9у² - 25 = 0.

Решим уравнение:

1. a) $$(2x - 5)^2 - (2x - 3)(2x + 3) = 0$$

   $$4x^2 - 20x + 25 - (4x^2 - 9) = 0$$

   $$4x^2 - 20x + 25 - 4x^2 + 9 = 0$$

   $$-20x + 34 = 0$$

   $$-20x = -34$$

   $$x = \frac{-34}{-20} = \frac{17}{10} = 1,7$$

2. б) $$9y^2 - 25 = 0$$

   $$9y^2 = 25$$

   $$y^2 = \frac{25}{9}$$

   $$y = \pm \sqrt{\frac{25}{9}} = \pm \frac{5}{3}$$

Ответ:

1. a) $$x = 1,7$$
2. б) $$y = \pm \frac{5}{3}$$