Решебник по алгебре 8 класс Мерзляк ФГОС Задание 545

 

\[\boxed{\mathbf{545\ (545).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 15 - x^{2} =\]

\[= (\sqrt{15} - x)(\sqrt{15} + x)\]

\[2)\ 49x² - 2 =\]

\[= (7x - \sqrt{2})(7x + \sqrt{2})\]

\[3)\ 36p - 64q =\]

\[= (6\sqrt{p} - 8\sqrt{q})(6\sqrt{p} + 8\sqrt{q})\]

\[4)\ c - 100 =\]

\[= (\sqrt{c} - 10)(\sqrt{c} + 10)\]

\[5)\ a - 8b\sqrt{a} + 16b^{2} =\]

\[= (\sqrt{a} - 4b)²\]

\[6)\ m + 2\sqrt{\text{mn}} + n =\]

\[= (\sqrt{m} + \sqrt{n})²\]

\[7)\ a - 4\sqrt{a} + 4 = (\sqrt{a} - 2)²\]

\[8)\ 5 + \sqrt{5} = \sqrt{5} \cdot (\sqrt{5} + 1)\]

\[9)\sqrt{3p} - p = \sqrt{p} \cdot (\sqrt{3} - \sqrt{p})\]

\[10)\ \sqrt{12} + \sqrt{32} = 2\sqrt{3} + 4\sqrt{2} =\]

\[= 2 \cdot (\sqrt{3} + 2\sqrt{2})\ \]

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

\[1)\ \sqrt{x^{2}} = x + 8\]

\[|x| = x + 8\]

\[x - x = 8,\ \ - x - x = 8\]

\[Ответ:\ x = - 4.\]

\[2)\ \sqrt{x^{2}} = 6x - 10\]

\[|x| = 6x - 10\]

\[x - 6x = - 10\]

\[- 5x = - 10\]

\[x = 2\]

\[Ответ:x = 2.\]