544. Найдите корни уравнения: а) (2x - 3)(5x + 1) = 2x + 2/5; б) (3x - 1)(x + 3) = x(1 + 6x). 545. Решите уравнение. 546. Решите уравнение.

544. а) $(2x - 3)(5x + 1) = 2x + \frac{2}{5}$ $10x^2 + 2x - 15x - 3 = 2x + 0,4$ $10x^2 - 15x - 3,4 = 0$ $D = (-15)^2 - 4 \cdot 10 \cdot (-3,4) = 225 + 136 = 361 = 19^2$ $x_1 = \frac{15 + 19}{20} = \frac{34}{20} = 1,7$; $x_2 = \frac{15 - 19}{20} = -\frac{4}{20} = -0,2$ Ответ: 1,7; -0,2. б) $(3x - 1)(x + 3) = x(1 + 6x)$ $3x^2 + 9x - x - 3 = x + 6x^2$ $3x^2 + 8x - 3 - x - 6x^2 = 0$ $-3x^2 + 7x - 3 = 0$ $3x^2 - 7x + 3 = 0$ $D = (-7)^2 - 4 \cdot 3 \cdot 3 = 49 - 36 = 13$ $x = \frac{7 \pm \sqrt{13}}{6}$ Ответ: $\frac{7 \pm \sqrt{13}}{6}$. 545. а) $(x + 4)^2 = 3x + 40$ $x^2 + 8x + 16 - 3x - 40 = 0$ $x^2 + 5x - 24 = 0$ По теореме Виета: $x_1 + x_2 = -5$; $x_1 \cdot x_2 = -24 \Rightarrow x_1 = -8, x_2 = 3$ Ответ: -8; 3. б) $(2x - 3)^2 = 11x - 19$ $4x^2 - 12x + 9 - 11x + 19 = 0$ $4x^2 - 23x + 28 = 0$ $D = (-23)^2 - 4 \cdot 4 \cdot 28 = 529 - 448 = 81 = 9^2$ $x_1 = \frac{23 + 9}{8} = 4$; $x_2 = \frac{23 - 9}{8} = \frac{14}{8} = 1,75$ Ответ: 4; 1,75. в) $3(x + 4)^2 = 10x + 32$ $3(x^2 + 8x + 16) - 10x - 32 = 0$ $3x^2 + 24x + 48 - 10x - 32 = 0$ $3x^2 + 14x + 16 = 0$ $D = 14^2 - 4 \cdot 3 \cdot 16 = 196 - 192 = 4 = 2^2$ $x_1 = \frac{-14 + 2}{6} = -2$; $x_2 = \frac{-14 - 2}{6} = -\frac{16}{6} = -2\frac{2}{3}$ Ответ: -2; $-2\frac{2}{3}$. г) $15x^2 + 17 = 15(x + 1)^2$ $15x^2 + 17 = 15(x^2 + 2x + 1)$ $15x^2 + 17 = 15x^2 + 30x + 15$ $30x = 2$ $x = \frac{2}{30} = \frac{1}{15}$ Ответ: $\frac{1}{15}$. 546. а) $\frac{x^2 - 1}{2} - 11x = 11$ $x^2 - 1 - 22x = 22$ $x^2 - 22x - 23 = 0$ По теореме Виета: $x_1 + x_2 = 22$; $x_1 \cdot x_2 = -23 \Rightarrow x_1 = 23, x_2 = -1$ Ответ: 23; -1. б) $\frac{x^2 + x}{2} = \frac{8x - 7}{3}$ $3(x^2 + x) = 2(8x - 7)$ $3x^2 + 3x = 16x - 14$ $3x^2 - 13x + 14 = 0$ $D = (-13)^2 - 4 \cdot 3 \cdot 14 = 169 - 168 = 1$ $x_1 = \frac{13 + 1}{6} = \frac{14}{6} = 2\frac{1}{3}$; $x_2 = \frac{13 - 1}{6} = 2$ Ответ: $2\frac{1}{3}$; 2.