![\lg(\textbf{x}^2-\textbf{x})=1-\lg5](https://tex.z-dn.net/?f=%5Clg%28%5Ctextbf%7Bx%7D%5E2-%5Ctextbf%7Bx%7D%29%3D1-%5Clg5)
Отметим ОДЗ:
![\textbf{x}^2-\textbf{x}>0 \\ \textbf{x}(\textbf{x}-1)>0](https://tex.z-dn.net/?f=%5Ctextbf%7Bx%7D%5E2-%5Ctextbf%7Bx%7D%3E0+%5C%5C+%5Ctextbf%7Bx%7D%28%5Ctextbf%7Bx%7D-1%29%3E0)
![\lg(\textbf{x}^2-\textbf{x})=\lg\textbf{2}](https://tex.z-dn.net/?f=%5Clg%28%5Ctextbf%7Bx%7D%5E2-%5Ctextbf%7Bx%7D%29%3D%5Clg%5Ctextbf%7B2%7D)
<em>
</em><em><u>Воспользуемся свойством логарифмов:
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</em></u><em><u>
По т. Виета
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![\left \{ {{\textbf{x}_1+\textbf{x}_2=2} \atop {\textbf{x}_1\cdot\textbf{x}_2=-2}} \right. \to \left \{ {{\textbf{x}_1=-1} \atop {\textbf{x}_2=2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B%5Ctextbf%7Bx%7D_1%2B%5Ctextbf%7Bx%7D_2%3D2%7D+%5Catop+%7B%5Ctextbf%7Bx%7D_1%5Ccdot%5Ctextbf%7Bx%7D_2%3D-2%7D%7D+%5Cright.+%5Cto+%5Cleft+%5C%7B+%7B%7B%5Ctextbf%7Bx%7D_1%3D-1%7D+%5Catop+%7B%5Ctextbf%7Bx%7D_2%3D2%7D%7D+%5Cright.+)
Произведение корней видно по т. Виета
<em><u />Ответ: -2.</em>
2x^2-18x+36=0
Д=324-4×2×36=36
х1=18+6/4=6
х2=18-6/4=3
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