519. Решите уравнение: a) 4x² – 3x + 7 = 2x² + x + 7; б) -5y² + 8y + 8 = 8y + 3; в) 10 – 3x² = x² + 10 – x; г) 1 – 2у + 3y² = y² – 2y + 1.

a) $$4x^2 - 3x + 7 = 2x^2 + x + 7$$

$$2x^2 - 4x = 0$$

$$2x(x-2) = 0$$

$$x_1 = 0, x_2 = 2$$

б) $$-5y^2 + 8y + 8 = 8y + 3$$

$$-5y^2 + 5 = 0$$

$$y^2 = 1$$

$$y = \pm 1$$

$$y_1 = 1, y_2 = -1$$

в) $$10 - 3x^2 = x^2 + 10 - x$$

$$-4x^2 + x = 0$$

$$x(-4x + 1) = 0$$

$$x_1 = 0, x_2 = \frac{1}{4} = 0,25$$

г) $$1 - 2y + 3y^2 = y^2 - 2y + 1$$

$$2y^2 = 0$$

$$y = 0$$

Ответ: а) $$x_1 = 0, x_2 = 2$$; б) $$y_1 = 1, y_2 = -1$$; в) $$x_1 = 0, x_2 = 0,25$$; г) $$y = 0$$