\[\boxed{\text{780.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{2} - 8x + k = 0\] \[\left\{ \begin{matrix} x_{1} + x_{2} = 8 \\ x_{1}x_{2} = k\ \ \ \ \ \ \\ \end{matrix} \right.\ \] |
\[3x_{1} + 4x_{2} = 29\] \[3x_{1} = 29 - 4x_{2}\] \[x_{1} = \frac{29 - 4x_{2}}{3}\ \] |
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\[\left\{ \begin{matrix} \frac{29 - 4x_{2}}{3} + x_{2} = 8\ \ \ | \cdot 3 \\ \frac{29 - 4x_{2}}{3} \cdot x_{2} = k\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} 29 - 4x_{2} + 3x_{2} = 24 \\ \frac{x_{2} \cdot \left( 29 - 4x_{2} \right)}{3} = k\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x_{2} = 5 \\ \frac{5 \cdot (29 - 4 \cdot 5)}{3} = k \\ \end{matrix} \right.\ \]
\[k = \frac{5 \cdot 9}{3} = 15\]
\[Ответ:k = 15.\ \]