вправа 736 гдз 7 клас алгебра Мерзляк Полонський
7 клас ➠ алгебра ➠ Мерзляк Полонський
Вправа 736
Відповідь:
\begin{equation}Якщо x_{1}-x_{2}=8, x_{1}x_{2}=5, то:\end{equation}
\begin{equation}1)x_{1}x_{2}^{2}-x_{1}^{2}x_{2}=\end{equation}
\begin{equation}=x_{1}x_{2}\cdot \left ( x_{2}-x_{1} \right )=\end{equation}
\begin{equation}=-x_{1}x_{2}\cdot \left ( x_{1}-x_{2} \right )=\end{equation}
\begin{equation}=-5\cdot 8=-40;\end{equation}
\begin{equation}2)x_{1}^{2}+x_{2}^{2}=\end{equation}
\begin{equation}=\left ( x_{1}-x_{2} \right )^{2}+2x_{1}x_{2}=\end{equation}
\begin{equation}=8^{2}+2\cdot 5=\end{equation}
\begin{equation}=64+10=74;\end{equation}
\begin{equation}3)\left ( x_{1}+x_{2} \right )^{2}=\end{equation}
\begin{equation}=\left ( x_{1}-x_{2} \right )^{2}+4x_{1}x_{2}=\end{equation}
\begin{equation}=8^{2}+4\cdot 5=\end{equation}
\begin{equation}=64+20=84;\end{equation}
\begin{equation}4) x_{1}^{3}-x_{2}^{3}=\end{equation}
\begin{equation}=\left ( x_{1}-x_{2} \right )\left ( x_{1}^{2}+x_{1}x_{2}+x_{2}^{2} \right )=\end{equation}
\begin{equation}=\left ( x_{1}-x_{2} \right )\left ( \left ( x_{1}-x_{2} \right )^{2}+3x_{1}x_{2} \right )=\end{equation}
\begin{equation}=8\cdot \left ( 8^{2}+3\cdot 5 \right )=\end{equation}
\begin{equation}=8\cdot 79=632.\end{equation}