Сумма квадратов корней уравнения 3х^2+ах-1=0равна 22/9. Найдите значение а.

Ответ:

\[3x^{2} + ax - 1 = 0\]

\[x^{2} + \frac{a}{3}x - \frac{1}{3} = 0\]

\[\text{\ \ }x_{1}^{2} + x_{2}^{2} = \frac{22}{9}\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{a}{3} \\ x_{1} \cdot x_{2} = - \frac{1}{3}\text{\ \ \ } \\ \end{matrix} \right.\ \]

\[\left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} = \frac{22}{9}\]

\[\left( - \frac{a}{3} \right)^{2} - 2 \cdot \left( - \frac{1}{3} \right) = \frac{22}{9}\]

\[\frac{a^{2}}{9} + \frac{2}{3} - \frac{22}{9} = 0\ \ \ \ \ | \cdot 9\]

\[a^{2} + 6 - 22 = 0\]

\[a^{2} - 16 = 0\]

\[a^{2} = 16\]

\[a = \pm 4\]

\[Ответ:\ при\ a = \pm 4.\]