126. Решите уравнение: 1) (4x + 1)(x - 3) = 12; 2) (x + 2)(x - 3) - (2x - 5)(x + 3) = x(x - 5); 3) (6x − 5)² + (3x - 2) (3x + 2) = 36.

Решим уравнения.

1) $$(4x + 1)(x - 3) = 12$$

$$4x^2 - 12x + x - 3 = 12$$

$$4x^2 - 11x - 15 = 0$$

$$D = (-11)^2 - 4 \cdot 4 \cdot (-15) = 121 + 240 = 361$$

$$x_1 = \frac{11 + \sqrt{361}}{2 \cdot 4} = \frac{11 + 19}{8} = \frac{30}{8} = \frac{15}{4} = 3.75$$

$$x_2 = \frac{11 - \sqrt{361}}{2 \cdot 4} = \frac{11 - 19}{8} = \frac{-8}{8} = -1$$

Ответ: 3,75; -1

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2) $$(x + 2)(x - 3) - (2x - 5)(x + 3) = x(x - 5)$$ $$x^2 - 3x + 2x - 6 - (2x^2 + 6x - 5x - 15) = x^2 - 5x$$

$$x^2 - x - 6 - 2x^2 - x + 15 = x^2 - 5x$$

$$-x^2 - 2x + 9 = x^2 - 5x$$

$$2x^2 - 3x - 9 = 0$$

$$D = (-3)^2 - 4 \cdot 2 \cdot (-9) = 9 + 72 = 81$$

$$x_1 = \frac{3 + \sqrt{81}}{2 \cdot 2} = \frac{3 + 9}{4} = \frac{12}{4} = 3$$

$$x_2 = \frac{3 - \sqrt{81}}{2 \cdot 2} = \frac{3 - 9}{4} = \frac{-6}{4} = -1.5$$

Ответ: 3; -1,5

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3) $$(6x - 5)^2 + (3x - 2) (3x + 2) = 36$$

$$36x^2 - 60x + 25 + 9x^2 - 4 = 36$$

$$45x^2 - 60x - 15 = 0$$

$$3x^2 - 4x - 1 = 0$$

$$D = (-4)^2 - 4 \cdot 3 \cdot (-1) = 16 + 12 = 28$$

$$x_1 = \frac{4 + \sqrt{28}}{2 \cdot 3} = \frac{4 + 2\sqrt{7}}{6} = \frac{2 + \sqrt{7}}{3}$$

$$x_2 = \frac{4 - \sqrt{28}}{2 \cdot 3} = \frac{4 - 2\sqrt{7}}{6} = \frac{2 - \sqrt{7}}{3}$$

Ответ: $$\frac{2 + \sqrt{7}}{3}$$; $$\frac{2 - \sqrt{7}}{3}$$