А7. Решите уравнения: а) 10-29x=3x²; 6) 17x² +34x = 0

Ответ: a) x = -10 и x = 1/3; б) x = 0 и x = -2

Решение:

a) \[10 - 29x = 3x^2\]

\[3x^2 + 29x - 10 = 0\]

Дискриминант: \[D = 29^2 - 4 \cdot 3 \cdot (-10) = 841 + 120 = 961\]

\[x_1 = \frac{-29 + \sqrt{961}}{2 \cdot 3} = \frac{-29 + 31}{6} = \frac{2}{6} = \frac{1}{3}\]

\[x_2 = \frac{-29 - \sqrt{961}}{2 \cdot 3} = \frac{-29 - 31}{6} = \frac{-60}{6} = -10\]

б) \[17x^2 + 34x = 0\]

\[17x(x + 2) = 0\]

\[x_1 = 0\]

\[x + 2 = 0 \Rightarrow x_2 = -2\]

Ответ: a) x = -10 и x = 1/3; б) x = 0 и x = -2