659. Решите уравнение: 1) x² − 4x + 3 = 0; 2) x² + 2x − 3 = 0; 3) x² + 3x − 4 = 0; 4) x² − 4x − 21 = 0; 5) x² + x − 56 = 0; 6) x² − 6x − 7 = 0; 7) x² − 8x + 12 = 0; 8) x² + 7x + 6 = 0; 9) -x² + 6x + 55 = 0; 10) 2x² − 3x − 2 = 0; 11) 2x² − x − 6 = 0; 12) 3x² − 4x − 20 = 0; 13) 10x² − 7x − 3 = 0; 14) -5x² + 7x - 2 = 0;

Решение уравнений:

1) x² − 4x + 3 = 0

\[D = (-4)^2 - 4 \cdot 1 \cdot 3 = 16 - 12 = 4\] \[x_1 = \frac{-(-4) + \sqrt{4}}{2 \cdot 1} = \frac{4 + 2}{2} = 3\] \[x_2 = \frac{-(-4) - \sqrt{4}}{2 \cdot 1} = \frac{4 - 2}{2} = 1\]

2) x² + 2x − 3 = 0

\[D = 2^2 - 4 \cdot 1 \cdot (-3) = 4 + 12 = 16\] \[x_1 = \frac{-2 + \sqrt{16}}{2 \cdot 1} = \frac{-2 + 4}{2} = 1\] \[x_2 = \frac{-2 - \sqrt{16}}{2 \cdot 1} = \frac{-2 - 4}{2} = -3\]

3) x² + 3x − 4 = 0

\[D = 3^2 - 4 \cdot 1 \cdot (-4) = 9 + 16 = 25\] \[x_1 = \frac{-3 + \sqrt{25}}{2 \cdot 1} = \frac{-3 + 5}{2} = 1\] \[x_2 = \frac{-3 - \sqrt{25}}{2 \cdot 1} = \frac{-3 - 5}{2} = -4\]

4) x² − 4x − 21 = 0

\[D = (-4)^2 - 4 \cdot 1 \cdot (-21) = 16 + 84 = 100\] \[x_1 = \frac{-(-4) + \sqrt{100}}{2 \cdot 1} = \frac{4 + 10}{2} = 7\] \[x_2 = \frac{-(-4) - \sqrt{100}}{2 \cdot 1} = \frac{4 - 10}{2} = -3\]

5) x² + x − 56 = 0

\[D = 1^2 - 4 \cdot 1 \cdot (-56) = 1 + 224 = 225\] \[x_1 = \frac{-1 + \sqrt{225}}{2 \cdot 1} = \frac{-1 + 15}{2} = 7\] \[x_2 = \frac{-1 - \sqrt{225}}{2 \cdot 1} = \frac{-1 - 15}{2} = -8\]

6) x² − 6x − 7 = 0

\[D = (-6)^2 - 4 \cdot 1 \cdot (-7) = 36 + 28 = 64\] \[x_1 = \frac{-(-6) + \sqrt{64}}{2 \cdot 1} = \frac{6 + 8}{2} = 7\] \[x_2 = \frac{-(-6) - \sqrt{64}}{2 \cdot 1} = \frac{6 - 8}{2} = -1\]

7) x² − 8x + 12 = 0

\[D = (-8)^2 - 4 \cdot 1 \cdot 12 = 64 - 48 = 16\] \[x_1 = \frac{-(-8) + \sqrt{16}}{2 \cdot 1} = \frac{8 + 4}{2} = 6\] \[x_2 = \frac{-(-8) - \sqrt{16}}{2 \cdot 1} = \frac{8 - 4}{2} = 2\]

8) x² + 7x + 6 = 0

\[D = 7^2 - 4 \cdot 1 \cdot 6 = 49 - 24 = 25\] \[x_1 = \frac{-7 + \sqrt{25}}{2 \cdot 1} = \frac{-7 + 5}{2} = -1\] \[x_2 = \frac{-7 - \sqrt{25}}{2 \cdot 1} = \frac{-7 - 5}{2} = -6\]

9) -x² + 6x + 55 = 0

\[x² - 6x - 55 = 0\] \[D = (-6)^2 - 4 \cdot 1 \cdot (-55) = 36 + 220 = 256\] \[x_1 = \frac{-(-6) + \sqrt{256}}{2 \cdot 1} = \frac{6 + 16}{2} = 11\] \[x_2 = \frac{-(-6) - \sqrt{256}}{2 \cdot 1} = \frac{6 - 16}{2} = -5\]

10) 2x² − 3x − 2 = 0

\[D = (-3)^2 - 4 \cdot 2 \cdot (-2) = 9 + 16 = 25\] \[x_1 = \frac{-(-3) + \sqrt{25}}{2 \cdot 2} = \frac{3 + 5}{4} = 2\] \[x_2 = \frac{-(-3) - \sqrt{25}}{2 \cdot 2} = \frac{3 - 5}{4} = -0.5\]

11) 2x² − x − 6 = 0

\[D = (-1)^2 - 4 \cdot 2 \cdot (-6) = 1 + 48 = 49\] \[x_1 = \frac{-(-1) + \sqrt{49}}{2 \cdot 2} = \frac{1 + 7}{4} = 2\] \[x_2 = \frac{-(-1) - \sqrt{49}}{2 \cdot 2} = \frac{1 - 7}{4} = -1.5\]

12) 3x² − 4x − 20 = 0

\[D = (-4)^2 - 4 \cdot 3 \cdot (-20) = 16 + 240 = 256\] \[x_1 = \frac{-(-4) + \sqrt{256}}{2 \cdot 3} = \frac{4 + 16}{6} = \frac{10}{3}\] \[x_2 = \frac{-(-4) - \sqrt{256}}{2 \cdot 3} = \frac{4 - 16}{6} = -2\]

13) 10x² − 7x − 3 = 0

\[D = (-7)^2 - 4 \cdot 10 \cdot (-3) = 49 + 120 = 169\] \[x_1 = \frac{-(-7) + \sqrt{169}}{2 \cdot 10} = \frac{7 + 13}{20} = 1\] \[x_2 = \frac{-(-7) - \sqrt{169}}{2 \cdot 10} = \frac{7 - 13}{20} = -0.3\]

14) -5x² + 7x - 2 = 0

\[5x² - 7x + 2 = 0\] \[D = (-7)^2 - 4 \cdot 5 \cdot 2 = 49 - 40 = 9\] \[x_1 = \frac{-(-7) + \sqrt{9}}{2 \cdot 5} = \frac{7 + 3}{10} = 1\] \[x_2 = \frac{-(-7) - \sqrt{9}}{2 \cdot 5} = \frac{7 - 3}{10} = 0.4\]

Ответ: Выше приведены решения уравнений.