Не решая уравнение 3x^2-7x-11=0, найдите значение выражения x_1^2+x_2^2.

\[3x^{2} - 7x - 11 = 0\]

\[x_{1} + x_{2} = \frac{7}{3};\ \ x_{1} \cdot x_{2} = - \frac{11}{3};\]

\[\left( x_{1} + x_{2} \right)^{2} = x_{1}^{2} + 2x_{1}x_{2} + x_{2}^{2} = \left( \frac{7}{3} \right)^{2}\]

\[x_{1}^{2} + x_{2}^{2} = \frac{49}{9} - 2 \cdot \left( - \frac{11}{3} \right) =\]

\[= \frac{49}{9} + \frac{22}{3} = \frac{49 + 66}{9} =\]

\[= \frac{115}{9} = 12\frac{7}{9}.\]

\[Ответ:\ \ 12\frac{7}{9}.\]