Найдите область определения функции y=6/(корень из (8+10x-3x^2)).

Ответ:

\[y = \frac{6}{\sqrt{8 + 10x - 3x^{2}}}\]

\[8 + 10x - 3x^{2} > 0\]

\[3x^{2} - 10x - 8 < 0\]

\[D = 25 + 24 = 49\]

\[x_{1} = \frac{5 + 7}{3} = 4;\ \ x_{2} = \frac{5 - 7}{3} = - \frac{2}{3}\]

\[3\left( x + \frac{2}{3} \right)(x - 4) < 0\]

\[D(y) = \left( - \frac{2}{3};4 \right).\]