13.1 Решите уравнение (3x - 5)^2 = (2x + 1)^2.

### 13.1 $(3x - 5)^2 = (2x + 1)^2$ $9x^2 - 30x + 25 = 4x^2 + 4x + 1$ $5x^2 - 34x + 24 = 0$ $D = (-34)^2 - 4 \cdot 5 \cdot 24 = 1156 - 480 = 676 = 26^2$ $x_1 = \frac{34 + 26}{10} = 6$ $x_2 = \frac{34 - 26}{10} = 0.8$ **Ответ: 0.8; 6.** ### 13.2 $9x^2 - 30x + 25 = (x - 2)^2$ $(3x - 5)^2 = (x - 2)^2$ $|3x - 5| = |x - 2|$ 1) $3x - 5 = x - 2 \Rightarrow 2x = 3 \Rightarrow x = 1.5$ 2) $3x - 5 = -(x - 2) \Rightarrow 3x - 5 = -x + 2 \Rightarrow 4x = 7 \Rightarrow x = 1.75$ **Ответ: 1.5; 1.75.** ### 13.3 $(x + 5)^2 = 2x^2 + 10x - 7$ $x^2 + 10x + 25 = 2x^2 + 10x - 7$ $x^2 = 32$ $x = \pm \sqrt{32} = \pm 4\sqrt{2}$ **Ответ: $-4\sqrt{2}; 4\sqrt{2}$.** ### 13.4 $5x^2 - 14x + 8 = 3x^2 - 14x + 16$ $2x^2 = 8$ $x^2 = 4$ $x = \pm 2$ **Ответ: -2; 2.** ### 13.5 $(4x + 1)^2 = 16x^2 + 20x + 5$ $16x^2 + 8x + 1 = 16x^2 + 20x + 5$ $-12x = 4$ $x = -\frac{1}{3}$ **Ответ: -1/3.** ### 13.6 $4x^2 + 28x + 49 = (x - 1)^2$ $(2x + 7)^2 = (x - 1)^2$ $|2x + 7| = |x - 1|$ 1) $2x + 7 = x - 1 \Rightarrow x = -8$ 2) $2x + 7 = -(x - 1) \Rightarrow 2x + 7 = -x + 1 \Rightarrow 3x = -6 \Rightarrow x = -2$ **Ответ: -8; -2.**