\[\boxed{\text{673\ (673).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[7x^{2} + bx - 23 = 0\ \ \ \ \ \ \ \ \ \ |\ :7\]
\[x^{2} + \frac{b}{7}x - \frac{23}{7} = 0\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = - \frac{b}{7} \\ x_{1}x_{2} = - \frac{23}{7}\text{\ \ \ } \\ \end{matrix} \right.\ \ \]
\[x_{1} > 0\]
\[x_{2} < 0\]
\[Что\ и\ требовалось\ доказать.\ \]
\[\boxed{\text{673.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\textbf{а)}\ x + 4xy = 5\ \]
\[вторая\ степень.\]
\[\textbf{б)}\ x^{5} + 8x^{3}y^{3} = 1\]
\[шестая\ степень.\]
\[\textbf{в)}\ 8x^{6} - y^{2} = 2x^{4} \cdot (4x^{2} - y)\]
\[8x^{6} - y^{2} = 8x^{6} - 2x^{4}y\]
\[2x^{4}y - y^{2} = 0\]
\[пятая\ степень.\]
\[\textbf{г)}\ (x - 2y)^{2} - x^{2} =\]
\[= 4y(y - x) + 5x\]
\[x^{2} - 4xy + 4y^{2} - x^{2} =\]
\[= 4y^{2} - 4xy + 5x\]
\[5x = 0\]
\[первая\ степень.\]