Решебник по алгебре 8 класс Мерзляк ФГОС Задание 873

 

\[\boxed{\mathbf{873\ (873).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{3x^{- 8}y^{5}z^{- 12}}{7a^{0}b^{- 3}c^{4}} = \frac{3b^{3}y^{5}}{7x^{8}z^{12}c^{4}}\]

\[2)\ \frac{1,001{^\circ}m^{- 15}n^{- 7}p^{- 4}}{2^{- 3}a^{- 11}b^{16}c^{- 22}} =\]

\[= \frac{8a^{11}c^{22}}{b^{16}m^{15}n^{7}p^{4}}\]

\[\boxed{\mathbf{8}\mathbf{73}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ (a + 3)(a + 1) > a(a + 4)\]

\[a^{2} + 3a + a + 3 - a^{2} - 4a > 0\]

\[3 > 0\]

\[чтд.\]

\[2)\ 3(b - 4) + 2b < 5b - 10\]

\[3b - 12 + 2b - 5b + 10 < 0\]

\[- 2 < 0\]

\[чтд.\]

\[3)\ (c - 4)(c + 4) > c^{2} - 20\]

\[c^{2} - 16 - c^{2} + 20 > 0\]

\[4 > 0\]

\[чтд.\]

\[4)\ x(x + 6) - x^{2} < 2(3x + 1)\]

\[x^{2} + 6x - x^{2} - 6x - 2 < 0\]

\[- 2 < 0\]

\[чтд.\]

\[5)\ (y + 5)(y - 2) \geq 3y - 10\]

\[y^{2} + 5y - 2y - 10 - 3y + 10 \geq 0\]

\[y^{2} \geq 0\]

\[чтд.\]

\[6)\ 8m^{2} - 6m + 1 \leq (3m - 1)^{2}\]

\[8m^{2} - 6m + 1 \leq 9m^{2} - 6m + 1\]

\[- m^{2} \leq 0\]

\[чтд.\]

\[7)\ a(a - 2) \geq - 1\]

\[a^{2} - 2a + 1 \geq 0\]

\[(a - 1)^{2} \geq 0\]

\[чтд.\]

\[8)\ (b + 7)^{2} > 14b + 40\]

\[b^{2} + 14b + 49 - 14b - 40 > 0\]

\[b^{2} + 9 > 0\]

\[чтд.\]