Решите уравнение: a) (3x + 1)³ = 27x²(x + 1) + 8x + 2; б) 4x²(2x + 9) = (2x + 3)³ + 12(3x + 1).

Решим уравнения:

a) $$(3x + 1)^3 = 27x^2(x + 1) + 8x + 2$$

$$27x^3 + 27x^2 + 9x + 1 = 27x^3 + 27x^2 + 8x + 2$$

$$27x^3 + 27x^2 + 9x + 1 - 27x^3 - 27x^2 - 8x - 2 = 0$$

$$x - 1 = 0$$

$$x = 1$$

б) $$4x^2(2x + 9) = (2x + 3)^3 + 12(3x + 1)$$

$$8x^3 + 36x^2 = (8x^3 + 36x^2 + 54x + 27) + (36x + 12)$$

$$8x^3 + 36x^2 = 8x^3 + 36x^2 + 54x + 27 + 36x + 12$$

$$8x^3 + 36x^2 - 8x^3 - 36x^2 - 54x - 27 - 36x - 12 = 0$$

$$-90x - 39 = 0$$

$$-90x = 39$$

$$x = -\frac{39}{90} = -\frac{13}{30}$$

Ответ: a) x = 1, б) x = -13/30