28.14 a) x² + 2x − 7 = 0; 6) 2x² − 4x - 1 = 0;

а) x² + 2x - 7 = 0

a = 1, b = 2, c = -7

$$D = b^2 - 4ac = 2^2 - 4 \cdot 1 \cdot (-7) = 4 + 28 = 32$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-2 + \sqrt{32}}{2 \cdot 1} = \frac{-2 + 4\sqrt{2}}{2} = -1 + 2\sqrt{2}$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-2 - \sqrt{32}}{2 \cdot 1} = \frac{-2 - 4\sqrt{2}}{2} = -1 - 2\sqrt{2}$$

б) 2x² - 4x - 1 = 0

a = 2, b = -4, c = -1

$$D = b^2 - 4ac = (-4)^2 - 4 \cdot 2 \cdot (-1) = 16 + 8 = 24$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{4 + \sqrt{24}}{2 \cdot 2} = \frac{4 + 2\sqrt{6}}{4} = 1 + \frac{\sqrt{6}}{2}$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{4 - \sqrt{24}}{2 \cdot 2} = \frac{4 - 2\sqrt{6}}{4} = 1 - \frac{\sqrt{6}}{2}$$

Ответ: a) x₁ = -1 + 2√2, x₂ = -1 - 2√2; б) x₁ = 1 + √6/2, x₂ = 1 - √6/2