550. Решите уравнение: а) x(5x - 3) = 3(2x - 1 1/3); б) (2x + 1)(x - 3) = x(4 - x) - 9; в) (3x - 2)(3x + 2) = 4x(x - 1); г) (1 - 2x)(2x + 1) = -2x(3x + 1) + 2; д) (2m + 3)^2 = (m - 1)(m + 1); е) 5a(a + 1) = (3a - 2)^2; ж) (2p + 3)^2 - (p - 1)^2 = -8; з) 3(2x - 1)^2 = 7x^2 + 12.

550. Решите уравнение: а) $x(5x - 3) = 3(2x - 1\frac{1}{3})$ $5x^2 - 3x = 6x - 4$ $5x^2 - 9x + 4 = 0$ $D = (-9)^2 - 4 \cdot 5 \cdot 4 = 81 - 80 = 1$ $x_1 = \frac{9 + 1}{10} = 1$; $x_2 = \frac{9 - 1}{10} = 0,8$ **Ответ: 0,8; 1** б) $(2x + 1)(x - 3) = x(4 - x) - 9$ $2x^2 - 6x + x - 3 = 4x - x^2 - 9$ $3x^2 - 9x + 6 = 0$ | $: 3$ $x^2 - 3x + 2 = 0$ По теореме Виета: $x_1 + x_2 = 3$, $x_1 \cdot x_2 = 2$ $x_1 = 1$; $x_2 = 2$ **Ответ: 1; 2** в) $(3x - 2)(3x + 2) = 4x(x - 1)$ $9x^2 - 4 = 4x^2 - 4x$ $5x^2 + 4x - 4 = 0$ $D/4 = 2^2 - 5 \cdot (-4) = 4 + 20 = 24$ $x = \frac{-2 \pm \sqrt{24}}{5} = \frac{-2 \pm 2\sqrt{6}}{5}$ **Ответ: \frac{-2 \pm 2\sqrt{6}}{5}** г) $(1 - 2x)(2x + 1) = -2x(3x + 1) + 2$ $1 - 4x^2 = -6x^2 - 2x + 2$ $2x^2 + 2x - 1 = 0$ $D/4 = 1^2 - 2 \cdot (-1) = 3$ $x = \frac{-1 \pm \sqrt{3}}{2}$ **Ответ: \frac{-1 \pm \sqrt{3}}{2}** д) $(2m + 3)^2 = (m - 1)(m + 1)$ $4m^2 + 12m + 9 = m^2 - 1$ $3m^2 + 12m + 10 = 0$ $D/4 = 6^2 - 3 \cdot 10 = 36 - 30 = 6$ $m = \frac{-6 \pm \sqrt{6}}{3} = -2 \pm \frac{\sqrt{6}}{3}$ **Ответ: -2 \pm \frac{\sqrt{6}}{3}** е) $5a(a + 1) = (3a - 2)^2$ $5a^2 + 5a = 9a^2 - 12a + 4$ $4a^2 - 17a + 4 = 0$ $D = 17^2 - 4 \cdot 4 \cdot 4 = 289 - 64 = 225 = 15^2$ $a_1 = \frac{17 + 15}{8} = 4$; $a_2 = \frac{17 - 15}{8} = 0,25$ **Ответ: 0,25; 4** ж) $(2p + 3)^2 - (p - 1)^2 = -8$ $4p^2 + 12p + 9 - (p^2 - 2p + 1) = -8$ $3p^2 + 14p + 16 = 0$ $D/4 = 7^2 - 3 \cdot 16 = 49 - 48 = 1$ $p_1 = \frac{-7 + 1}{3} = -2$; $p_2 = \frac{-7 - 1}{3} = -2\frac{2}{3}$ **Ответ: -2\frac{2}{3}; -2** з) $3(2x - 1)^2 = 7x^2 + 12$ $3(4x^2 - 4x + 1) = 7x^2 + 12$ $12x^2 - 12x + 3 = 7x^2 + 12$ $5x^2 - 12x - 9 = 0$ $D/4 = (-6)^2 - 5 \cdot (-9) = 36 + 45 = 81 = 9^2$ $x_1 = \frac{6 + 9}{5} = 3$; $x_2 = \frac{6 - 9}{5} = -0,6$ **Ответ: -0,6; 3**