Для каждого значения а решите уравнение: x^2-(5a+7)x+35a=0.

Ответ:

\[x² - (5a + 7)x + 35a = 0\]

\[D = (5a + 7)^{2} - 4 \cdot 1 \cdot 35a =\]

\[= 25a^{2} + 70a + 49 - 140a =\]

\[= 25a^{2} - 70a + 49 = (5a - 7)^{2}\]

\[x_{1,2} = \frac{5a + 7 \pm \sqrt{(5a - 7)^{2}}}{2} =\]

\[= \frac{5a + 7 \pm |5a - 7|}{2}\]

\[1)\ a = 1,4:\]

\[x = \frac{5 \cdot 1,4 + 7 \pm |5 \cdot 1,4 - 7|}{2} =\]

\[= \frac{7 + 7 \pm 0}{2} = \frac{14}{2} = 7.\]

\[2)\ a > 1,4:\]

\[x_{1} = \frac{5a + 7 + 5a - 7}{2} =\]

\[= \frac{10a}{2} = 5a;\]

\[x_{2} = \frac{5a + 7 - 5a + 7}{2} = \frac{14}{2} = 7.\]

\[Ответ:\ \ a = 1,4 \Longrightarrow x = 7;\ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a \neq 1,4 \Longrightarrow x_{1} = 5a;\ \ \]

\[x_{2} = 7.\]