Для каждого значения а решите уравнение: 4(a+1)x^2+(a-3)x-1=0.

\[4 \cdot (a + 1)x² + (a - 3)x - 1 = 0\]

\[= a^{2} - 6a + 9 + 16a + 16 =\]

\[= a^{2} + 10a + 25 = (a + 5)^{2}\]

\[При\ D = 0:\]

\[(a + 5)^{2} = 0\]

\[a + 5 = 0\]

\[a = - 5.\]

\[1)\ a = - 5:\]

\[x = \frac{3 - ( - 5) \pm | - 5 + 5|}{8 \cdot ( - 5 + 1)} =\]

\[3)\ \ a > - 5:\]

\[x_{1} = \frac{3 - a + a + 5}{8 \cdot (a + 1)} =\]

\[x_{2} = \frac{3 - a - a - 5}{8 \cdot (a + 1)} =\]

\[= \frac{- 2a - 2}{8 \cdot (a + 1)} =\]

\[Ответ:\ a = - 5 \Longrightarrow \ x = - \frac{1}{4};\ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ a > - 5 \Longrightarrow \ x_{1} = \frac{1}{a + 1};\ \ \ \]

\[x_{2} = - \frac{1}{4}.\]