\[\boxed{\text{773.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[2x^{2} - 5x + c = 0\] \[x^{2} - 2,5x + \frac{c}{2} = 0\ \ \] |
\[x_{2}^{2} - x_{1}^{2} = 0,25\ \ \Longrightarrow \left( x_{2} - x_{1} \right)\left( x_{2} + x_{1} \right) = 0,25\] \[\left( x_{2} - x_{1} \right) \cdot 2,5 = 0,25\] \[x_{2} - x_{1} = 0,1 \Longrightarrow x_{2} = 0,1 + x_{1}\ \] |
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\[\left\{ \begin{matrix} x_{1} + x_{2} = 2,5 \\ x_{1}x_{2} = \frac{c}{2}\text{\ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} x_{1} + x_{1} + 0,1 = 2,5 \\ x_{1}x_{2} = 0,5c\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 2x_{1} = 2,4 \\ x_{1}x_{2} = 0,5c \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x_{1} = 1,2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x_{1}\left( x_{1} + 0,1 \right) = 0,5c \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[1,2 \cdot (1,2 + 0,1) = 0,5c\ \ \ \ \ \ \]
\[\ |\ :0,5\]
\[c = 1,2 \cdot 1,3\ :0,5 = 3,12\]
\[Ответ:c = 3,12.\ \]