Решебник по алгебре 8 класс Мерзляк ФГОС Задание 542

 

\[\boxed{\mathbf{542\ (542).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{4}{\sqrt{2}} = \frac{4\sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{4\sqrt{2}}{2} = 2\sqrt{2};\]

\[2)\frac{12}{\sqrt{6}} = \frac{12\sqrt{6}}{\sqrt{6} \cdot \sqrt{6}} = \frac{12\sqrt{6}}{6} = 2\sqrt{6};\]

\[3)\frac{18}{\sqrt{5}} = \frac{18\sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{18\sqrt{5}}{5};\]

\[4)\frac{m}{\sqrt{n}} = \frac{m\sqrt{n}}{\sqrt{n} \cdot \sqrt{n}} = \frac{m\sqrt{n}}{n};\]

\[5)\frac{a}{b\sqrt{b}} = \frac{a\sqrt{b}}{b \cdot \sqrt{b} \cdot \sqrt{b}} = \frac{a\sqrt{b}}{b^{2}};\ \]

\[6)\frac{5}{\sqrt{15}} = \frac{5\sqrt{15}}{15} = \frac{\sqrt{15}}{3};\]

\[7)\frac{7}{\sqrt{7}} = \frac{7\sqrt{7}}{7} = \sqrt{7};\]

\[8)\frac{24}{5\sqrt{3}} = \frac{24\sqrt{3}}{15} = \frac{8\sqrt{3}}{5}.\]

\[\boxed{\mathbf{5}\mathbf{4}\mathbf{2}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ y = \sqrt{x^{2}} - x,\ \ если\ x \leq 0\]

\[y = |x| - x\]

\[y = - x - x\]

\[y = - 2x\]

\[x = 0,\ \ y = 0\]

\[x = - 1,\ \ y = 2\]

\[2)\ y = 2x + \sqrt{x^{2}}\]

\[y = 2x + |x|\]

\[y = \left\{ \begin{matrix} 3x,\ \ x \geq 0 \\ x,\ \ x < 0\ \\ \end{matrix} \right.\ \]

\[3)\ y = \sqrt{x} \cdot \sqrt{x},\ \ x \geq 0\]

\[y = \sqrt{x^{2}},\ \ y = |x|\]

\[4)\ y = \frac{x^{2}}{\sqrt{x^{2}}} + 3\]

\[y = \frac{x^{2}}{|x|} + 3\ \]

\[y = \left\{ \begin{matrix} x + 3,\ \ x \geq 0 \\ - x + 3,\ \ x < 0 \\ \end{matrix} \right.\ \]